A von Karman plate with 1:1 internal resonance

Contents

In this example, we consider a simply-supported von Karman square plate subject to harmonic excitation. Due to the geometric symmetry, the natural frequenices of the second and the third modes are the same. In other words, the system has 1:1 internal resonance between the two modes. We extract the forced response curve using SSM reduction.

Geometry and finite element model

We discretize the plate with 200 elements and then 606 degrees-of-freedom. The dimension of the phase space of the full system is then 1212. As we will see, the reduced-order model obtained by SSM reduction is four dimensional.

clear all; close all; clc

l = 1; % length of domain [m]
b = 1;  % breadth of domain [m]
t = 1e-2; % thickness of plate [m]
w = 0.0; % curvature parameter (height of the midpoint relative to ends) [m]
% material properties
E     = 70e9;  % 70e9 % 200e9 % Young's modulus [Pa]
rho   = 2700; % 2700 % 7850 % density [kg/m^3]
nu    = 0.33;    % Poisson's ratio
kappa = 1e5; % material damping modulus 1e8

% Mesh
nElements = 10;
nl = nElements;
nb = nElements;
bc = 'SSSS';
startFE = tic;
[M,C,K,fnl,~,outdof] = build_model(l,b,t,w,E,rho,nu,kappa,bc,nl,nb);
timeFE = toc(startFE);
varargout{1} = timeFE;
n  = length(M);

Building FE model
Assembling M,C,K matrices
Applying boundary conditions
Solving undamped eigenvalue problem
The circular natural frequencies of the first five modes:

omega =

   1.0e+03 *

    0.3067
    0.7636
    0.7677
    1.2188
    1.5311

Using Rayleigh damping
Getting nonlinearity coefficients
Loaded tensors from storage
Assembling external force vector

Dynamical System Setup

notation = 'multiindex';
DSorder = 2;
DS = DynamicalSystem(DSorder);
set(DS,'M',M,'C',C,'K',K,'fnl',fnl);
set(DS.Options,'Emax',5,'Nmax',10,'notation',notation);

Linear Modal analysis

[V,D,W] = DS.linear_spectral_analysis();

Due to high-dimensionality, we compute only the first 5 eigenvalues with the smallest magnitude. These would also be used to compute the spectral quotients
Assuming a proportional damping hypthesis with symmetric matrices
modal damping ratio for 1 mode is 2.243693e-03
modal damping ratio for 2 mode is 2.181986e-03
modal damping ratio for 3 mode is 2.186754e-03
modal damping ratio for 4 mode is 2.847788e-03
modal damping ratio for 5 mode is 3.388843e-03
the left eigenvectors may be incorrect in case of asymmetry of matrices

 The first 10 nonzero eigenvalues are given as 
   1.0e+03 *

  -0.0007 + 0.3067i
  -0.0007 - 0.3067i
  -0.0017 + 0.7636i
  -0.0017 - 0.7636i
  -0.0017 + 0.7677i
  -0.0017 - 0.7677i
  -0.0035 + 1.2188i
  -0.0035 - 1.2188i
  -0.0052 + 1.5311i
  -0.0052 - 1.5311i

Add forcing

f_0 = zeros(n,1);
f_0(outdof(1)) = 100;
kappas  = [-1; 1];
epsilon = 1;
coeffs  = epsilon * [f_0 f_0]/2;
DS.add_forcing(coeffs, kappas);

Primiary resonance with IRs

Create SSM

S = SSM(DS);
set(S.Options, 'reltol', 0.8,'notation',notation); % 0.8 is used

Extract FRC

Recall that the natural frequencies of the linear modes are given by

$\omega_{(i,j)}=\left(\frac{i^2}{l^2}+\frac{j^2}{b^2}\right)\pi^2\sqrt{\frac{D}{\rho t}}$

where $D$ is the bending stiffness. Given $l=b$, we have $\omega_{(1,2)}=\omega_{(2,1)}$, namely the 1:1 internal resonance between the second and the third bending modes. In addition, we have $\omega_{(3,1)}=\omega_{(1,3)}=2\omega_{(1,2)}$, which implies that the higher modes (1,3) and (3,1) will also be taken as a part of the spectral subspace in the extract_FRC routine. Here we are mainly concerned with the 1:1 internal resonance. So we need to specify the spectral subspace, which can be easily done in the SSM-ep toolbox.

set(S.contOptions, 'PtMX', 2500, 'h_max', 5, 'h_min', 1e-4);
set(S.FRCOptions, 'initialSolver', 'fsolve');
set(S.Options, 'COMPtype', 'first');
freqrange = [0.95 1.15]*imag(D(3));
order     = 5;
resonant_modes = [3 4 5 6];
mFreq   = [1 1];
FRC_lead = S.SSM_isol2ep('isol_polar',resonant_modes, order, mFreq, 'freq', freqrange,outdof);

(near) outer resonance detected for the following combination of master eigenvalues
     0     0     1     1
     0     1     1     0
     1     0     0     1
     1     1     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     1
     0     1     1     0
     1     0     0     1
     1     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     0
     1     0     1     0
     2     0     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     0     2
     0     1     0     1
     0     2     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     0
     1     0     1     0
     2     0     0     0
     0     0     0     2
     0     1     0     1
     0     2     0     0

These are in resonance with the follwing eigenvalues of the slave subspace
   1.0e+03 *

  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0052 + 1.5311i
  -0.0052 + 1.5311i
  -0.0052 + 1.5311i
  -0.0052 - 1.5311i
  -0.0052 - 1.5311i
  -0.0052 - 1.5311i

sigma_out = 3
(near) inner resonance detected for the following combination of master eigenvalues
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0

These are in resonance with the follwing eigenvalues of the master subspace
   1.0e+02 *

  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i

sigma_in = 3
Due to (near) outer resonance, the exisitence of the manifold is questionable and the underlying computation may suffer.
Attempting manifold computation
Manifold computation time at order 2 = 00:00:00
Estimated memory usage at order  2 = 1.64E+00 MB
Manifold computation time at order 3 = 00:00:00
Estimated memory usage at order  3 = 3.53E+00 MB
Manifold computation time at order 4 = 00:00:00
Estimated memory usage at order  4 = 8.23E+00 MB
Manifold computation time at order 5 = 00:00:01
Estimated memory usage at order  5 = 1.56E+01 MB

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


 Run='isol_polar.ep': Continue equilibria along primary branch.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          7.58e-14  1.08e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE            om         rho1         rho2          th1          th2          eps
    0  00:00:00   1.0799e+03      1  EP      7.6359e+02   5.6525e-03   1.9407e-02   5.7177e+00   6.1050e+00   1.0000e+00
   10  00:00:00   1.0709e+03      2          7.5722e+02   3.2006e-03   1.3569e-02   6.0791e+00   6.1532e+00   1.0000e+00
   20  00:00:00   1.0591e+03      3          7.4886e+02   1.7765e-03   8.8062e-03   6.1762e+00   6.1987e+00   1.0000e+00
   30  00:00:00   1.0461e+03      4          7.3962e+02   1.1422e-03   6.1231e-03   6.2149e+00   6.2245e+00   1.0000e+00
   40  00:00:01   1.0309e+03      5          7.2888e+02   7.9882e-04   4.4789e-03   6.2355e+00   6.2403e+00   1.0000e+00
   43  00:00:01   1.0260e+03      6  EP      7.2541e+02   7.2746e-04   4.1180e-03   6.2398e+00   6.2437e+00   1.0000e+00

 STEP      TIME        ||U||  LABEL  TYPE            om         rho1         rho2          th1          th2          eps
    0  00:00:01   1.0799e+03      7  EP      7.6359e+02   5.6525e-03   1.9407e-02   5.7177e+00   6.1050e+00   1.0000e+00
   10  00:00:01   1.0891e+03      8          7.7009e+02   1.7568e-02   2.5856e-02   4.4176e+00   6.0206e+00   1.0000e+00
   20  00:00:01   1.1120e+03      9          7.8625e+02   3.8789e-02   3.8407e-02   3.8956e+00   5.5869e+00   1.0000e+00
   30  00:00:01   1.1303e+03     10          7.9923e+02   5.0569e-02   4.6326e-02   3.2506e+00   4.9418e+00   1.0000e+00
   38  00:00:01   1.1303e+03     11  SN      7.9925e+02   5.0600e-02   4.6248e-02   3.2296e+00   4.9220e+00   1.0000e+00
   38  00:00:01   1.1303e+03     12  FP      7.9925e+02   5.0600e-02   4.6248e-02   3.2296e+00   4.9220e+00   1.0000e+00
   40  00:00:01   1.1303e+03     13          7.9925e+02   5.0603e-02   4.6231e-02   3.2255e+00   4.9182e+00   1.0000e+00
   50  00:00:01   1.1303e+03     14          7.9922e+02   5.0608e-02   4.6108e-02   3.2009e+00   4.8952e+00   1.0000e+00
   60  00:00:02   1.1291e+03     15          7.9838e+02   5.0095e-02   4.4793e-02   3.0584e+00   4.7653e+00   1.0000e+00
   70  00:00:02   1.1107e+03     16          7.8539e+02   3.9564e-02   2.6301e-02   2.4029e+00   4.5186e+00   1.0000e+00
   80  00:00:02   1.1105e+03     17          7.8524e+02   3.9254e-02   2.5432e-02   2.3778e+00   4.5801e+00   1.0000e+00
   83  00:00:02   1.1105e+03     18  FP      7.8524e+02   3.9243e-02   2.5397e-02   2.3767e+00   4.5838e+00   1.0000e+00
   83  00:00:02   1.1105e+03     19  SN      7.8524e+02   3.9243e-02   2.5397e-02   2.3767e+00   4.5838e+00   1.0000e+00
   90  00:00:02   1.1105e+03     20          7.8524e+02   3.9205e-02   2.5282e-02   2.3729e+00   4.5971e+00   1.0000e+00
  100  00:00:02   1.1107e+03     21          7.8533e+02   3.9113e-02   2.4994e-02   2.3618e+00   4.6469e+00   1.0000e+00
  101  00:00:02   1.1107e+03     22  HB      7.8537e+02   3.9101e-02   2.4955e-02   2.3598e+00   4.6588e+00   1.0000e+00
  109  00:00:02   1.1161e+03     23  HB      7.8915e+02   3.7319e-02   3.1193e-02   2.4732e+00   5.2751e+00   1.0000e+00
  110  00:00:02   1.1161e+03     24          7.8920e+02   3.7009e-02   3.1595e-02   2.4857e+00   5.2984e+00   1.0000e+00
  119  00:00:03   1.1162e+03     25  SN      7.8923e+02   3.6429e-02   3.2250e-02   2.5073e+00   5.3364e+00   1.0000e+00
  119  00:00:03   1.1162e+03     26  FP      7.8923e+02   3.6429e-02   3.2250e-02   2.5073e+00   5.3364e+00   1.0000e+00
  120  00:00:03   1.1162e+03     27          7.8923e+02   3.6384e-02   3.2297e-02   2.5089e+00   5.3391e+00   1.0000e+00
  130  00:00:03   1.1161e+03     28          7.8921e+02   3.5928e-02   3.2737e-02   2.5245e+00   5.3650e+00   1.0000e+00
  140  00:00:03   1.1155e+03     29          7.8872e+02   3.3197e-02   3.4665e-02   2.6027e+00   5.4826e+00   1.0000e+00
  150  00:00:03   1.1114e+03     30          7.8584e+02   2.0155e-02   3.9652e-02   2.8038e+00   5.7492e+00   1.0000e+00
  160  00:00:03   1.1114e+03     31  FP      7.8584e+02   1.9750e-02   3.9822e-02   2.8066e+00   5.7533e+00   1.0000e+00
  160  00:00:03   1.1114e+03     32  SN      7.8584e+02   1.9750e-02   3.9822e-02   2.8066e+00   5.7533e+00   1.0000e+00
  160  00:00:03   1.1114e+03     33          7.8584e+02   1.9736e-02   3.9828e-02   2.8067e+00   5.7534e+00   1.0000e+00
  170  00:00:03   1.1114e+03     34          7.8584e+02   1.9547e-02   3.9910e-02   2.8079e+00   5.7552e+00   1.0000e+00
  180  00:00:03   1.1114e+03     35          7.8586e+02   1.8826e-02   4.0234e-02   2.8122e+00   5.7616e+00   1.0000e+00
  190  00:00:03   1.1181e+03     36          7.9059e+02   1.0356e-02   4.7326e-02   2.7930e+00   5.7668e+00   1.0000e+00
  200  00:00:03   1.1527e+03     37          8.1505e+02   4.0486e-03   6.8562e-02   2.5661e+00   5.5291e+00   1.0000e+00
  210  00:00:04   1.1952e+03     38          8.4512e+02   1.3226e-03   9.1518e-02   2.3347e+00   5.0949e+00   1.0000e+00
  220  00:00:04   1.2046e+03     39          8.5176e+02   6.5094e-04   9.6629e-02   2.5392e+00   4.8891e+00   1.0000e+00
  230  00:00:04   1.2068e+03     40          8.5330e+02   4.7128e-04   9.7770e-02   2.9452e+00   4.7897e+00   1.0000e+00
  240  00:00:04   1.2074e+03     41          8.5377e+02   4.5790e-04   9.8055e-02   3.3578e+00   4.7195e+00   1.0000e+00
  245  00:00:04   1.2075e+03     42  FP      8.5381e+02   4.8224e-04   9.8048e-02   3.5119e+00   4.6908e+00   1.0000e+00
  245  00:00:04   1.2075e+03     43  SN      8.5381e+02   4.8224e-04   9.8048e-02   3.5119e+00   4.6908e+00   1.0000e+00
  250  00:00:04   1.2075e+03     44          8.5379e+02   5.0713e-04   9.8001e-02   3.6039e+00   4.6711e+00   1.0000e+00
  260  00:00:04   1.2072e+03     45          8.5358e+02   5.8734e-04   9.7750e-02   3.7755e+00   4.6238e+00   1.0000e+00
  270  00:00:04   1.2035e+03     46          8.5100e+02   9.7567e-04   9.5346e-02   4.0041e+00   4.4587e+00   1.0000e+00
  280  00:00:04   1.1610e+03     47          8.2093e+02   2.4592e-03   7.0422e-02   3.7533e+00   3.9090e+00   1.0000e+00
  290  00:00:04   1.1199e+03     48          7.9186e+02   2.9292e-03   4.2311e-02   3.4592e+00   3.5624e+00   1.0000e+00
  300  00:00:05   1.1047e+03     49          7.8115e+02   2.2021e-03   2.1104e-02   3.2885e+00   3.3454e+00   1.0000e+00
  310  00:00:05   1.1046e+03     50          7.8109e+02   2.1110e-03   1.9724e-02   3.2796e+00   3.3319e+00   1.0000e+00
  313  00:00:05   1.1046e+03     51  FP      7.8109e+02   2.1088e-03   1.9692e-02   3.2794e+00   3.3316e+00   1.0000e+00
  313  00:00:05   1.1046e+03     52  SN      7.8109e+02   2.1088e-03   1.9692e-02   3.2794e+00   3.3316e+00   1.0000e+00
  320  00:00:05   1.1046e+03     53          7.8109e+02   2.1008e-03   1.9574e-02   3.2786e+00   3.3304e+00   1.0000e+00
  330  00:00:05   1.1047e+03     54          7.8110e+02   2.0753e-03   1.9207e-02   3.2763e+00   3.3268e+00   1.0000e+00
  340  00:00:05   1.1062e+03     55          7.8221e+02   1.7142e-03   1.4549e-02   3.2474e+00   3.2815e+00   1.0000e+00
  350  00:00:05   1.1145e+03     56          7.8805e+02   1.1850e-03   9.0407e-03   3.2127e+00   3.2283e+00   1.0000e+00
  360  00:00:05   1.1269e+03     57          7.9685e+02   8.5007e-04   6.1084e-03   3.1924e+00   3.2001e+00   1.0000e+00
  370  00:00:05   1.1425e+03     58          8.0782e+02   6.3453e-04   4.3968e-03   3.1795e+00   3.1837e+00   1.0000e+00
  380  00:00:05   1.1607e+03     59          8.2074e+02   4.8987e-04   3.3153e-03   3.1708e+00   3.1733e+00   1.0000e+00
  390  00:00:06   1.1817e+03     60          8.3555e+02   3.8868e-04   2.5883e-03   3.1648e+00   3.1664e+00   1.0000e+00
  400  00:00:06   1.2052e+03     61          8.5221e+02   3.1546e-04   2.0768e-03   3.1604e+00   3.1615e+00   1.0000e+00
  410  00:00:06   1.2316e+03     62          8.7087e+02   2.6054e-04   1.7006e-03   3.1571e+00   3.1579e+00   1.0000e+00
  414  00:00:06   1.2419e+03     63  EP      8.7813e+02   2.4401e-04   1.5886e-03   3.1561e+00   3.1568e+00   1.0000e+00
the forcing frequency 7.2541e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.2654e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.2776e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.2888e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.3007e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.3116e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.3231e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.3338e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.3449e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.3552e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.3660e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.3760e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.3864e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.3962e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.4063e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.4158e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.4255e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.4348e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.4442e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.4532e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.4624e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.4711e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.4800e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.4886e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.4973e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5057e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5142e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5224e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5308e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5390e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5473e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5555e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5639e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5722e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5807e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5893e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.5982e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6075e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6174e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6265e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6314e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6339e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6352e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6359e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6359e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6366e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6379e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6404e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6452e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6516e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6589e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6733e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6810e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.6912e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.7009e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.7114e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.7232e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.7358e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.7500e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.7650e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.7815e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.7991e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8182e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8389e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8625e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8899e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9218e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9570e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9747e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9830e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9909e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9918e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9920e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9922e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9924e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9924e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9924e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9924e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9925e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9925e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9925e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9925e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9925e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9925e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9925e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9925e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9924e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9924e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9924e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9924e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9924e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9924e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9924e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9922e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9921e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9920e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9919e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9917e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9914e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9910e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9903e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9893e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9874e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9838e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9770e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9640e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9416e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9240e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9072e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8913e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8761e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8617e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8556e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8539e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8530e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8528e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8526e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8525e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8525e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8524e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8525e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8525e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8525e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8526e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8526e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8527e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8527e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8529e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8531e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8533e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8537e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8537e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8544e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8556e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8579e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8622e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8705e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8862e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8898e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8915e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8916e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8920e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8922e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8922e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8923e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8922e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8922e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8922e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8921e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8921e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8920e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8919e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8918e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8916e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8913e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8909e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8902e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8891e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8872e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8835e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8773e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8714e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8657e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8604e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8591e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8586e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8585e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8584e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8585e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8585e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8586e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8588e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8591e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8597e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8608e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8629e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8669e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8745e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8826e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8942e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9059e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9212e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9362e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9548e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9728e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9945e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0188e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0471e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0798e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1152e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1505e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1859e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2212e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2566e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2919e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3273e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3626e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3963e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4167e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4344e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4512e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4654e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4758e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4856e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4921e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4982e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5034e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5078e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5116e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5148e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5176e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5201e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5222e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5241e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5259e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5274e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5288e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5300e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5312e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5322e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5330e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5338e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5344e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5350e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5354e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5359e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5363e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5367e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5370e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5374e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5377e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5379e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5380e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5381e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5381e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5381e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5381e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5381e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5381e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5381e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5380e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5380e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5379e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5378e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5377e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5376e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5375e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5373e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5371e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5369e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5366e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5362e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5358e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5352e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5344e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5333e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5318e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5299e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5278e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5249e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5213e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5165e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5100e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5004e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4854e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4568e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4214e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3861e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3507e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3154e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2800e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2447e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2093e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1740e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1386e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1033e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0679e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0326e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0013e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9757e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9542e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9359e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9186e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9022e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8865e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8717e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8576e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8442e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8337e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8248e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8187e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8138e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8115e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8112e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8109e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8110e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8110e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8110e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8111e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8112e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8113e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8117e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8123e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8135e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8157e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8186e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8221e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8261e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8306e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8355e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8409e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8467e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8527e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8593e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8660e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8732e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8805e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8883e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.8961e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9044e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9128e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9216e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9305e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9398e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9490e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9588e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9685e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9787e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9888e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 7.9995e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0100e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0210e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0319e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0434e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0547e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0666e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0782e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.0906e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1025e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1153e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1276e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1408e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1534e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1670e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1800e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.1940e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2074e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2218e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2355e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2503e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2644e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2796e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.2940e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3096e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3244e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3403e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3555e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3718e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.3873e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4040e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4199e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4370e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4532e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4707e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.4873e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5051e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5221e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5403e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5576e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5762e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.5939e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.6128e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.6312e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.6502e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.6693e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.6888e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.7087e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.7290e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.7497e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.7708e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02
the forcing frequency 8.7813e+02 is nearly resonant with the eigenvalue -1.6662e+00 + i7.6359e+02

varargout =

  1×1 cell array

    {1×1 struct}

We explore the contribution of non-autonomous part SSM

set(S.Options, 'contribNonAuto',false);
FRC_zero = S.SSM_isol2ep('isol_polar_zero',resonant_modes, order, mFreq, 'freq', freqrange,outdof);

(near) outer resonance detected for the following combination of master eigenvalues
     0     0     1     1
     0     1     1     0
     1     0     0     1
     1     1     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     1
     0     1     1     0
     1     0     0     1
     1     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     0
     1     0     1     0
     2     0     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     0     2
     0     1     0     1
     0     2     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     0
     1     0     1     0
     2     0     0     0
     0     0     0     2
     0     1     0     1
     0     2     0     0

These are in resonance with the follwing eigenvalues of the slave subspace
   1.0e+03 *

  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0052 + 1.5311i
  -0.0052 + 1.5311i
  -0.0052 + 1.5311i
  -0.0052 - 1.5311i
  -0.0052 - 1.5311i
  -0.0052 - 1.5311i

sigma_out = 3
(near) inner resonance detected for the following combination of master eigenvalues
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0

These are in resonance with the follwing eigenvalues of the master subspace
   1.0e+02 *

  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i

sigma_in = 3
Due to (near) outer resonance, the exisitence of the manifold is questionable and the underlying computation may suffer.
Attempting manifold computation
Manifold computation time at order 2 = 00:00:00
Estimated memory usage at order  2 = 1.64E+00 MB
Manifold computation time at order 3 = 00:00:00
Estimated memory usage at order  3 = 3.53E+00 MB
Manifold computation time at order 4 = 00:00:00
Estimated memory usage at order  4 = 8.23E+00 MB
Manifold computation time at order 5 = 00:00:01
Estimated memory usage at order  5 = 1.56E+01 MB

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


 Run='isol_polar_zero.ep': Continue equilibria along primary branch.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          7.58e-14  1.08e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE            om         rho1         rho2          th1          th2          eps
    0  00:00:00   1.0799e+03      1  EP      7.6359e+02   5.6525e-03   1.9407e-02   5.7177e+00   6.1050e+00   1.0000e+00
   10  00:00:00   1.0709e+03      2          7.5722e+02   3.2006e-03   1.3569e-02   6.0791e+00   6.1532e+00   1.0000e+00
   20  00:00:00   1.0591e+03      3          7.4886e+02   1.7765e-03   8.8062e-03   6.1762e+00   6.1987e+00   1.0000e+00
   30  00:00:00   1.0461e+03      4          7.3962e+02   1.1422e-03   6.1231e-03   6.2149e+00   6.2245e+00   1.0000e+00
   40  00:00:00   1.0309e+03      5          7.2888e+02   7.9882e-04   4.4789e-03   6.2355e+00   6.2403e+00   1.0000e+00
   43  00:00:00   1.0260e+03      6  EP      7.2541e+02   7.2746e-04   4.1180e-03   6.2398e+00   6.2437e+00   1.0000e+00

 STEP      TIME        ||U||  LABEL  TYPE            om         rho1         rho2          th1          th2          eps
    0  00:00:00   1.0799e+03      7  EP      7.6359e+02   5.6525e-03   1.9407e-02   5.7177e+00   6.1050e+00   1.0000e+00
   10  00:00:00   1.0891e+03      8          7.7009e+02   1.7568e-02   2.5856e-02   4.4176e+00   6.0206e+00   1.0000e+00
   20  00:00:00   1.1120e+03      9          7.8625e+02   3.8789e-02   3.8407e-02   3.8956e+00   5.5869e+00   1.0000e+00
   30  00:00:00   1.1303e+03     10          7.9923e+02   5.0569e-02   4.6326e-02   3.2506e+00   4.9418e+00   1.0000e+00
   38  00:00:01   1.1303e+03     11  SN      7.9925e+02   5.0600e-02   4.6248e-02   3.2296e+00   4.9220e+00   1.0000e+00
   38  00:00:01   1.1303e+03     12  FP      7.9925e+02   5.0600e-02   4.6248e-02   3.2296e+00   4.9220e+00   1.0000e+00
   40  00:00:01   1.1303e+03     13          7.9925e+02   5.0603e-02   4.6231e-02   3.2255e+00   4.9182e+00   1.0000e+00
   50  00:00:01   1.1303e+03     14          7.9922e+02   5.0608e-02   4.6108e-02   3.2009e+00   4.8952e+00   1.0000e+00
   60  00:00:01   1.1291e+03     15          7.9838e+02   5.0095e-02   4.4793e-02   3.0584e+00   4.7653e+00   1.0000e+00
   70  00:00:01   1.1107e+03     16          7.8539e+02   3.9564e-02   2.6301e-02   2.4029e+00   4.5186e+00   1.0000e+00
   80  00:00:01   1.1105e+03     17          7.8524e+02   3.9254e-02   2.5432e-02   2.3778e+00   4.5801e+00   1.0000e+00
   83  00:00:01   1.1105e+03     18  FP      7.8524e+02   3.9243e-02   2.5397e-02   2.3767e+00   4.5838e+00   1.0000e+00
   83  00:00:01   1.1105e+03     19  SN      7.8524e+02   3.9243e-02   2.5397e-02   2.3767e+00   4.5838e+00   1.0000e+00
   90  00:00:01   1.1105e+03     20          7.8524e+02   3.9205e-02   2.5282e-02   2.3729e+00   4.5971e+00   1.0000e+00
  100  00:00:01   1.1107e+03     21          7.8533e+02   3.9113e-02   2.4994e-02   2.3618e+00   4.6469e+00   1.0000e+00
  101  00:00:01   1.1107e+03     22  HB      7.8537e+02   3.9101e-02   2.4955e-02   2.3598e+00   4.6588e+00   1.0000e+00
  109  00:00:01   1.1161e+03     23  HB      7.8915e+02   3.7319e-02   3.1193e-02   2.4732e+00   5.2751e+00   1.0000e+00
  110  00:00:02   1.1161e+03     24          7.8920e+02   3.7009e-02   3.1595e-02   2.4857e+00   5.2984e+00   1.0000e+00
  119  00:00:02   1.1162e+03     25  SN      7.8923e+02   3.6429e-02   3.2250e-02   2.5073e+00   5.3364e+00   1.0000e+00
  119  00:00:02   1.1162e+03     26  FP      7.8923e+02   3.6429e-02   3.2250e-02   2.5073e+00   5.3364e+00   1.0000e+00
  120  00:00:02   1.1162e+03     27          7.8923e+02   3.6384e-02   3.2297e-02   2.5089e+00   5.3391e+00   1.0000e+00
  130  00:00:02   1.1161e+03     28          7.8921e+02   3.5928e-02   3.2737e-02   2.5245e+00   5.3650e+00   1.0000e+00
  140  00:00:02   1.1155e+03     29          7.8872e+02   3.3197e-02   3.4665e-02   2.6027e+00   5.4826e+00   1.0000e+00
  150  00:00:02   1.1114e+03     30          7.8584e+02   2.0155e-02   3.9652e-02   2.8038e+00   5.7492e+00   1.0000e+00
  160  00:00:02   1.1114e+03     31  FP      7.8584e+02   1.9750e-02   3.9822e-02   2.8066e+00   5.7533e+00   1.0000e+00
  160  00:00:02   1.1114e+03     32  SN      7.8584e+02   1.9750e-02   3.9822e-02   2.8066e+00   5.7533e+00   1.0000e+00
  160  00:00:02   1.1114e+03     33          7.8584e+02   1.9736e-02   3.9828e-02   2.8067e+00   5.7534e+00   1.0000e+00
  170  00:00:02   1.1114e+03     34          7.8584e+02   1.9547e-02   3.9910e-02   2.8079e+00   5.7552e+00   1.0000e+00
  180  00:00:02   1.1114e+03     35          7.8586e+02   1.8826e-02   4.0234e-02   2.8122e+00   5.7616e+00   1.0000e+00
  190  00:00:02   1.1181e+03     36          7.9059e+02   1.0356e-02   4.7326e-02   2.7930e+00   5.7668e+00   1.0000e+00
  200  00:00:03   1.1527e+03     37          8.1505e+02   4.0486e-03   6.8562e-02   2.5661e+00   5.5291e+00   1.0000e+00
  210  00:00:03   1.1952e+03     38          8.4512e+02   1.3226e-03   9.1518e-02   2.3347e+00   5.0949e+00   1.0000e+00
  220  00:00:03   1.2046e+03     39          8.5176e+02   6.5094e-04   9.6629e-02   2.5392e+00   4.8891e+00   1.0000e+00
  230  00:00:03   1.2068e+03     40          8.5330e+02   4.7128e-04   9.7770e-02   2.9452e+00   4.7897e+00   1.0000e+00
  240  00:00:03   1.2074e+03     41          8.5377e+02   4.5790e-04   9.8055e-02   3.3578e+00   4.7195e+00   1.0000e+00
  245  00:00:03   1.2075e+03     42  FP      8.5381e+02   4.8224e-04   9.8048e-02   3.5119e+00   4.6908e+00   1.0000e+00
  245  00:00:03   1.2075e+03     43  SN      8.5381e+02   4.8224e-04   9.8048e-02   3.5119e+00   4.6908e+00   1.0000e+00
  250  00:00:03   1.2075e+03     44          8.5379e+02   5.0713e-04   9.8001e-02   3.6039e+00   4.6711e+00   1.0000e+00
  260  00:00:03   1.2072e+03     45          8.5358e+02   5.8734e-04   9.7750e-02   3.7755e+00   4.6238e+00   1.0000e+00
  270  00:00:03   1.2035e+03     46          8.5100e+02   9.7567e-04   9.5346e-02   4.0041e+00   4.4587e+00   1.0000e+00
  280  00:00:03   1.1610e+03     47          8.2093e+02   2.4592e-03   7.0422e-02   3.7533e+00   3.9090e+00   1.0000e+00
  290  00:00:04   1.1199e+03     48          7.9186e+02   2.9292e-03   4.2311e-02   3.4592e+00   3.5624e+00   1.0000e+00
  300  00:00:04   1.1047e+03     49          7.8115e+02   2.2021e-03   2.1104e-02   3.2885e+00   3.3454e+00   1.0000e+00
  310  00:00:04   1.1046e+03     50          7.8109e+02   2.1110e-03   1.9724e-02   3.2796e+00   3.3319e+00   1.0000e+00
  313  00:00:04   1.1046e+03     51  FP      7.8109e+02   2.1088e-03   1.9692e-02   3.2794e+00   3.3316e+00   1.0000e+00
  313  00:00:04   1.1046e+03     52  SN      7.8109e+02   2.1088e-03   1.9692e-02   3.2794e+00   3.3316e+00   1.0000e+00
  320  00:00:04   1.1046e+03     53          7.8109e+02   2.1008e-03   1.9574e-02   3.2786e+00   3.3304e+00   1.0000e+00
  330  00:00:04   1.1047e+03     54          7.8110e+02   2.0753e-03   1.9207e-02   3.2763e+00   3.3268e+00   1.0000e+00
  340  00:00:04   1.1062e+03     55          7.8221e+02   1.7142e-03   1.4549e-02   3.2474e+00   3.2815e+00   1.0000e+00
  350  00:00:04   1.1145e+03     56          7.8805e+02   1.1850e-03   9.0407e-03   3.2127e+00   3.2283e+00   1.0000e+00
  360  00:00:04   1.1269e+03     57          7.9685e+02   8.5007e-04   6.1084e-03   3.1924e+00   3.2001e+00   1.0000e+00
  370  00:00:04   1.1425e+03     58          8.0782e+02   6.3453e-04   4.3968e-03   3.1795e+00   3.1837e+00   1.0000e+00
  380  00:00:04   1.1607e+03     59          8.2074e+02   4.8987e-04   3.3153e-03   3.1708e+00   3.1733e+00   1.0000e+00
  390  00:00:05   1.1817e+03     60          8.3555e+02   3.8868e-04   2.5883e-03   3.1648e+00   3.1664e+00   1.0000e+00
  400  00:00:05   1.2052e+03     61          8.5221e+02   3.1546e-04   2.0768e-03   3.1604e+00   3.1615e+00   1.0000e+00
  410  00:00:05   1.2316e+03     62          8.7087e+02   2.6054e-04   1.7006e-03   3.1571e+00   3.1579e+00   1.0000e+00
  414  00:00:05   1.2419e+03     63  EP      8.7813e+02   2.4401e-04   1.5886e-03   3.1561e+00   3.1568e+00   1.0000e+00

varargout =

  1×1 cell array

    {1×1 struct}

comparision of results

FRCs = {FRC_lead,FRC_zero};
thm = struct();
thm.SN = {'LineStyle', 'none', 'LineWidth', 2, ...
  'Color', 'cyan', 'Marker', 'o', 'MarkerSize', 8, 'MarkerEdgeColor', ...
  'cyan', 'MarkerFaceColor', 'white'};
thm.HB = {'LineStyle', 'none', 'LineWidth', 2, ...
  'Color', 'black', 'Marker', 's', 'MarkerSize', 8, 'MarkerEdgeColor', ...
  'black', 'MarkerFaceColor', 'white'};
color = {'r','k','m','b','g'};
figure;
ax1 = gca;
for k=1:2
    FRC = FRCs{k};
    SNidx = FRC.SNidx;
    HBidx = FRC.HBidx;
    FRC.st = double(FRC.st);
    FRC.st(HBidx) = nan;
    FRC.st(SNidx) = nan;
    % color
    ST = cell(2,1);
    ST{1} = {[color{k},'--'],'LineWidth',1.5}; % unstable
    ST{2} = {[color{k},'-'],'LineWidth',1.5};  % stable
    if k==1
    legs = 'SSM (TV)-$\mathcal{O}(5)$-unstable';
    legu = 'SSM (TV)-$\mathcal{O}(5)$-stable';
    else
    legs = 'SSM (TI)-$\mathcal{O}(5)$-unstable';
    legu = 'SSM (TI)-$\mathcal{O}(5)$-stable';
    end
    hold(ax1,'on');
    plot_stab_lines(FRC.om,FRC.Aout_frc(:,1),FRC.st,ST,legs,legu);
    SNfig = plot(FRC.om(SNidx),FRC.Aout_frc(SNidx,1),thm.SN{:});
    set(get(get(SNfig,'Annotation'),'LegendInformation'),...
    'IconDisplayStyle','off');
    HBfig = plot(FRC.om(HBidx),FRC.Aout_frc(HBidx,1),thm.HB{:});
    set(get(get(HBfig,'Annotation'),'LegendInformation'),...
    'IconDisplayStyle','off');
    xlabel('$\Omega$','Interpreter','latex');
    ylabel('$||w_A||_{\infty}$','Interpreter','latex');
    set(gca,'FontSize',14);
    grid on; axis tight;
end
legend boxoff
% Extract of ridges and trenches
% We extract ridges of trenches of the FRS of $||w_\mathrm{A}||_{\mathcal{L}^2}$

startwa = tic
optdof = outdof(1);
set(S.contOptions, 'PtMX', 450);  % continuation setting
epsRange = [0.01 1.0]*epsilon;
parRange = {freqrange,epsRange};
sol = ep_read_solution('','isol_polar.ep',1);
set(S.FRSOptions, 'calFRS', true);
set(S.FRCOptions,'DBCobjnorm','l2','DBCstepFactor', [10 100]);
S.extract_ridges_trenches('bcssm-dof1',resonant_modes,order,mFreq,parRange,outdof(1),optdof,{sol.p,sol.x});
timings.wa = toc(startwa)

startwa =

  uint64

   41431348275458

(near) outer resonance detected for the following combination of master eigenvalues
     0     0     1     1
     0     1     1     0
     1     0     0     1
     1     1     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     1
     0     1     1     0
     1     0     0     1
     1     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     0
     1     0     1     0
     2     0     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     0     2
     0     1     0     1
     0     2     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     0
     1     0     1     0
     2     0     0     0
     0     0     0     2
     0     1     0     1
     0     2     0     0

These are in resonance with the follwing eigenvalues of the slave subspace
   1.0e+03 *

  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0052 + 1.5311i
  -0.0052 + 1.5311i
  -0.0052 + 1.5311i
  -0.0052 - 1.5311i
  -0.0052 - 1.5311i
  -0.0052 - 1.5311i

sigma_out = 3
(near) inner resonance detected for the following combination of master eigenvalues
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0

These are in resonance with the follwing eigenvalues of the master subspace
   1.0e+02 *

  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i

sigma_in = 3
Due to (near) outer resonance, the exisitence of the manifold is questionable and the underlying computation may suffer.
Attempting manifold computation
Manifold computation time at order 2 = 00:00:00
Estimated memory usage at order  2 = 1.64E+00 MB
Manifold computation time at order 3 = 00:00:00
Estimated memory usage at order  3 = 3.53E+00 MB
Manifold computation time at order 4 = 00:00:00
Estimated memory usage at order  4 = 8.23E+00 MB
Manifold computation time at order 5 = 00:00:01
Estimated memory usage at order  5 = 1.56E+01 MB

Equation solved at initial point.

fsolve completed because the vector of function values at the initial point
is near zero as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


 Run='bcssm-dof1.freq.frc': Continue equilibria along primary branch.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          7.58e-14  1.08e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE           obj        d.obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.0799e+03      1  EP      6.8199e-04   0.0000e+00   7.6359e+02   0.0000e+00   5.6525e-03   1.9407e-02   5.7177e+00   6.1050e+00   1.0000e+00
   10  00:00:00   1.0709e+03      2          4.7525e-04   0.0000e+00   7.5722e+02   0.0000e+00   3.2006e-03   1.3569e-02   6.0791e+00   6.1532e+00   1.0000e+00
   20  00:00:01   1.0591e+03      3          3.0720e-04   0.0000e+00   7.4886e+02   0.0000e+00   1.7765e-03   8.8062e-03   6.1762e+00   6.1987e+00   1.0000e+00
   30  00:00:01   1.0461e+03      4          2.1319e-04   0.0000e+00   7.3962e+02   0.0000e+00   1.1422e-03   6.1231e-03   6.2149e+00   6.2245e+00   1.0000e+00
   40  00:00:01   1.0309e+03      5          1.5578e-04   0.0000e+00   7.2888e+02   0.0000e+00   7.9882e-04   4.4789e-03   6.2355e+00   6.2403e+00   1.0000e+00
   43  00:00:01   1.0260e+03      6  EP      1.4319e-04   0.0000e+00   7.2541e+02   0.0000e+00   7.2746e-04   4.1180e-03   6.2398e+00   6.2437e+00   1.0000e+00

 STEP      TIME        ||U||  LABEL  TYPE           obj        d.obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:01   1.0799e+03      7  EP      6.8199e-04   0.0000e+00   7.6359e+02   0.0000e+00   5.6525e-03   1.9407e-02   5.7177e+00   6.1050e+00   1.0000e+00
   10  00:00:02   1.0891e+03      8          8.7084e-04   0.0000e+00   7.7009e+02   0.0000e+00   1.7568e-02   2.5856e-02   4.4176e+00   6.0206e+00   1.0000e+00
   20  00:00:02   1.1120e+03      9          1.2700e-03   0.0000e+00   7.8625e+02   0.0000e+00   3.8789e-02   3.8407e-02   3.8956e+00   5.5869e+00   1.0000e+00
   26  00:00:03   1.1299e+03     10  FP      1.5251e-03   0.0000e+00   7.9896e+02   0.0000e+00   5.0280e-02   4.6425e-02   3.3276e+00   5.0152e+00   1.0000e+00
   26  00:00:03   1.1300e+03     11  BP      1.5251e-03   0.0000e+00   7.9900e+02   0.0000e+00   5.0318e-02   4.6427e-02   3.3205e+00   5.0083e+00   1.0000e+00
   30  00:00:03   1.1303e+03     12          1.5210e-03   0.0000e+00   7.9923e+02   0.0000e+00   5.0569e-02   4.6326e-02   3.2506e+00   4.9418e+00   1.0000e+00
   38  00:00:04   1.1303e+03     13  SN      1.5183e-03   0.0000e+00   7.9925e+02   0.0000e+00   5.0600e-02   4.6248e-02   3.2296e+00   4.9220e+00   1.0000e+00
   40  00:00:04   1.1303e+03     14          1.5177e-03   0.0000e+00   7.9925e+02   0.0000e+00   5.0603e-02   4.6231e-02   3.2255e+00   4.9182e+00   1.0000e+00
   50  00:00:04   1.1303e+03     15          1.5134e-03   0.0000e+00   7.9922e+02   0.0000e+00   5.0608e-02   4.6108e-02   3.2009e+00   4.8952e+00   1.0000e+00
   60  00:00:04   1.1291e+03     16          1.4688e-03   0.0000e+00   7.9838e+02   0.0000e+00   5.0095e-02   4.4793e-02   3.0584e+00   4.7653e+00   1.0000e+00
   70  00:00:05   1.1107e+03     17          7.9363e-04   0.0000e+00   7.8539e+02   0.0000e+00   3.9564e-02   2.6301e-02   2.4029e+00   4.5186e+00   1.0000e+00
   80  00:00:05   1.1105e+03     18          7.4920e-04   0.0000e+00   7.8524e+02   0.0000e+00   3.9254e-02   2.5432e-02   2.3778e+00   4.5801e+00   1.0000e+00
   83  00:00:06   1.1105e+03     19  SN      7.4716e-04   0.0000e+00   7.8524e+02   0.0000e+00   3.9243e-02   2.5397e-02   2.3767e+00   4.5838e+00   1.0000e+00
   90  00:00:06   1.1105e+03     20          7.4026e-04   0.0000e+00   7.8524e+02   0.0000e+00   3.9205e-02   2.5282e-02   2.3729e+00   4.5971e+00   1.0000e+00
  100  00:00:06   1.1107e+03     21          7.1980e-04   0.0000e+00   7.8533e+02   0.0000e+00   3.9113e-02   2.4994e-02   2.3618e+00   4.6469e+00   1.0000e+00
  101  00:00:06   1.1107e+03     22  HB      7.1603e-04   0.0000e+00   7.8537e+02   0.0000e+00   3.9101e-02   2.4955e-02   2.3598e+00   4.6588e+00   1.0000e+00
  105  00:00:07   1.1117e+03     23  FP      6.9552e-04   0.0000e+00   7.8606e+02   0.0000e+00   3.9079e-02   2.5138e-02   2.3497e+00   4.8025e+00   1.0000e+00
  105  00:00:07   1.1117e+03     24  BP      6.9552e-04   0.0000e+00   7.8606e+02   0.0000e+00   3.9079e-02   2.5140e-02   2.3497e+00   4.8028e+00   1.0000e+00
  109  00:00:07   1.1161e+03     25  HB      8.5862e-04   0.0000e+00   7.8915e+02   0.0000e+00   3.7319e-02   3.1193e-02   2.4732e+00   5.2751e+00   1.0000e+00
  110  00:00:07   1.1161e+03     26          8.7253e-04   0.0000e+00   7.8920e+02   0.0000e+00   3.7009e-02   3.1595e-02   2.4857e+00   5.2984e+00   1.0000e+00
  119  00:00:08   1.1162e+03     27  SN      8.9574e-04   0.0000e+00   7.8923e+02   0.0000e+00   3.6429e-02   3.2250e-02   2.5073e+00   5.3364e+00   1.0000e+00
  120  00:00:08   1.1162e+03     28          8.9742e-04   0.0000e+00   7.8923e+02   0.0000e+00   3.6384e-02   3.2297e-02   2.5089e+00   5.3391e+00   1.0000e+00
  130  00:00:08   1.1161e+03     29          9.1350e-04   0.0000e+00   7.8921e+02   0.0000e+00   3.5928e-02   3.2737e-02   2.5245e+00   5.3650e+00   1.0000e+00
  140  00:00:08   1.1155e+03     30          9.8846e-04   0.0000e+00   7.8872e+02   0.0000e+00   3.3198e-02   3.4664e-02   2.6027e+00   5.4826e+00   1.0000e+00
  150  00:00:09   1.1114e+03     31          1.2179e-03   0.0000e+00   7.8584e+02   0.0000e+00   2.0155e-02   3.9652e-02   2.8038e+00   5.7492e+00   1.0000e+00
  160  00:00:09   1.1114e+03     32  SN      1.2255e-03   0.0000e+00   7.8584e+02   0.0000e+00   1.9750e-02   3.9822e-02   2.8066e+00   5.7533e+00   1.0000e+00
  160  00:00:09   1.1114e+03     33          1.2258e-03   0.0000e+00   7.8584e+02   0.0000e+00   1.9736e-02   3.9828e-02   2.8067e+00   5.7534e+00   1.0000e+00
  170  00:00:10   1.1114e+03     34          1.2294e-03   0.0000e+00   7.8584e+02   0.0000e+00   1.9548e-02   3.9910e-02   2.8079e+00   5.7552e+00   1.0000e+00
  180  00:00:10   1.1114e+03     35          1.2436e-03   0.0000e+00   7.8586e+02   0.0000e+00   1.8833e-02   4.0231e-02   2.8121e+00   5.7616e+00   1.0000e+00
  190  00:00:10   1.1180e+03     36          1.5148e-03   0.0000e+00   7.9054e+02   0.0000e+00   1.0389e-02   4.7277e-02   2.7934e+00   5.7671e+00   1.0000e+00
  200  00:00:11   1.1525e+03     37          2.2077e-03   0.0000e+00   8.1491e+02   0.0000e+00   4.0652e-03   6.8452e-02   2.5673e+00   5.5307e+00   1.0000e+00
  210  00:00:11   1.1951e+03     38          2.9055e-03   0.0000e+00   8.4506e+02   0.0000e+00   1.3272e-03   9.1477e-02   2.3347e+00   5.0961e+00   1.0000e+00
  220  00:00:11   1.2046e+03     39          3.0589e-03   0.0000e+00   8.5175e+02   0.0000e+00   6.5267e-04   9.6618e-02   2.5374e+00   4.8898e+00   1.0000e+00
  230  00:00:12   1.2068e+03     40          3.0938e-03   0.0000e+00   8.5330e+02   0.0000e+00   4.7182e-04   9.7766e-02   2.9421e+00   4.7902e+00   1.0000e+00
  240  00:00:12   1.2074e+03     41          3.1032e-03   0.0000e+00   8.5377e+02   0.0000e+00   4.5757e-04   9.8055e-02   3.3545e+00   4.7201e+00   1.0000e+00
  243  00:00:12   1.2075e+03     42  BP      3.1036e-03   0.0000e+00   8.5380e+02   0.0000e+00   4.7053e-04   9.8059e-02   3.4521e+00   4.7024e+00   1.0000e+00
  246  00:00:12   1.2075e+03     43  SN      3.1034e-03   0.0000e+00   8.5381e+02   0.0000e+00   4.8224e-04   9.8048e-02   3.5119e+00   4.6908e+00   1.0000e+00
  250  00:00:13   1.2075e+03     44          3.1024e-03   0.0000e+00   8.5379e+02   0.0000e+00   5.0675e-04   9.8002e-02   3.6028e+00   4.6713e+00   1.0000e+00
  260  00:00:13   1.2072e+03     45          3.0959e-03   0.0000e+00   8.5358e+02   0.0000e+00   5.8632e-04   9.7754e-02   3.7740e+00   4.6243e+00   1.0000e+00
  270  00:00:13   1.2036e+03     46          3.0294e-03   0.0000e+00   8.5105e+02   0.0000e+00   9.7022e-04   9.5392e-02   4.0033e+00   4.4608e+00   1.0000e+00
  280  00:00:14   1.1613e+03     47          2.3049e-03   0.0000e+00   8.2116e+02   0.0000e+00   2.4522e-03   7.0614e-02   3.7555e+00   3.9119e+00   1.0000e+00
  290  00:00:14   1.1200e+03     48          1.4273e-03   0.0000e+00   7.9195e+02   0.0000e+00   2.9301e-03   4.2426e-02   3.4603e+00   3.5636e+00   1.0000e+00
  300  00:00:14   1.1047e+03     49          7.1919e-04   0.0000e+00   7.8114e+02   0.0000e+00   2.1954e-03   2.1000e-02   3.2879e+00   3.3444e+00   1.0000e+00
  310  00:00:15   1.1046e+03     50          6.7641e-04   0.0000e+00   7.8109e+02   0.0000e+00   2.1117e-03   1.9733e-02   3.2796e+00   3.3320e+00   1.0000e+00
  313  00:00:15   1.1046e+03     51  SN      6.7501e-04   0.0000e+00   7.8109e+02   0.0000e+00   2.1088e-03   1.9692e-02   3.2794e+00   3.3316e+00   1.0000e+00
  320  00:00:15   1.1046e+03     52          6.7136e-04   0.0000e+00   7.8109e+02   0.0000e+00   2.1014e-03   1.9584e-02   3.2787e+00   3.3305e+00   1.0000e+00
  330  00:00:16   1.1047e+03     53          6.6005e-04   0.0000e+00   7.8110e+02   0.0000e+00   2.0783e-03   1.9250e-02   3.2766e+00   3.3273e+00   1.0000e+00
  340  00:00:16   1.1060e+03     54          5.1464e-04   0.0000e+00   7.8201e+02   0.0000e+00   1.7497e-03   1.4967e-02   3.2500e+00   3.2856e+00   1.0000e+00
  350  00:00:16   1.1140e+03     55          3.1817e-04   0.0000e+00   7.8771e+02   0.0000e+00   1.2043e-03   9.2210e-03   3.2139e+00   3.2300e+00   1.0000e+00
  360  00:00:16   1.1263e+03     56          2.1445e-04   0.0000e+00   7.9642e+02   0.0000e+00   8.6168e-04   6.2043e-03   3.1931e+00   3.2011e+00   1.0000e+00
  370  00:00:17   1.1418e+03     57          1.5405e-04   0.0000e+00   8.0733e+02   0.0000e+00   6.4178e-04   4.4524e-03   3.1799e+00   3.1842e+00   1.0000e+00
  380  00:00:17   1.1599e+03     58          1.1600e-04   0.0000e+00   8.2018e+02   0.0000e+00   4.9470e-04   3.3506e-03   3.1711e+00   3.1737e+00   1.0000e+00
  390  00:00:17   1.1808e+03     59          9.0480e-05   0.0000e+00   8.3492e+02   0.0000e+00   3.9208e-04   2.6124e-03   3.1650e+00   3.1666e+00   1.0000e+00
  400  00:00:18   1.2042e+03     60          7.2553e-05   0.0000e+00   8.5150e+02   0.0000e+00   3.1799e-04   2.0942e-03   3.1606e+00   3.1616e+00   1.0000e+00
  410  00:00:18   1.2305e+03     61          5.9389e-05   0.0000e+00   8.7007e+02   0.0000e+00   2.6249e-04   1.7138e-03   3.1572e+00   3.1580e+00   1.0000e+00
  414  00:00:18   1.2419e+03     62  EP      5.5053e-05   0.0000e+00   8.7813e+02   0.0000e+00   2.4401e-04   1.5886e-03   3.1561e+00   3.1568e+00   1.0000e+00
Backbone curve along branch point (BP) 11

 Run='bcssm-dof1.freq.bp1': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.1300e+03      1  EP      0.0000e+00   1.5251e-03   7.9900e+02   0.0000e+00   5.0318e-02   4.6427e-02   3.3205e+00   5.0083e+00   1.0000e+00
    5  00:00:00   1.1300e+03      2  EP      1.0000e+00   1.5250e-03   7.9899e+02  -1.6860e-03   5.0315e-02   4.6423e-02   3.3205e+00   5.0083e+00   1.0000e+00

 Run='bcssm-dof1.freq.bc1': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          8.48e-14  1.13e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.1300e+03      1  EP     -1.6860e-03   1.5250e-03   7.9899e+02   1.0000e+00   5.0315e-02   4.6423e-02   3.3205e+00   5.0083e+00   1.0000e+00
   10  00:00:00   1.1077e+03      2         -2.0264e-03   1.0596e-03   7.8326e+02   7.4651e-01   3.6523e-02   3.2460e-02   3.3423e+00   5.1338e+00   1.0000e+00
   14  00:00:00   1.0963e+03      3  FP     -2.3165e-03   7.6867e-04   7.7514e+02   6.1296e-01   2.6688e-02   2.4173e-02   3.4006e+00   5.3702e+00   1.0000e+00
   20  00:00:01   1.0884e+03      4         -1.0127e-03   6.1118e-04   7.6961e+02   5.2729e-01   1.5728e-02   1.9420e-02   3.5512e+00   5.7234e+00   1.0000e+00
   30  00:00:01   1.0884e+03      5         -9.8168e-04   6.1001e-04   7.6960e+02   5.2612e-01   1.5633e-02   1.9398e-02   3.5425e+00   5.7238e+00   1.0000e+00
   40  00:00:01   1.0884e+03      6         -9.6654e-04   6.0958e-04   7.6960e+02   5.2567e-01   1.5601e-02   1.9393e-02   3.5372e+00   5.7235e+00   1.0000e+00
   50  00:00:01   1.0886e+03      7         -8.8555e-04   6.0927e-04   7.6972e+02   5.2537e-01   1.5632e-02   1.9455e-02   3.4981e+00   5.7160e+00   1.0000e+00
   54  00:00:02   1.0899e+03      8  SN     -7.0533e-04   6.2020e-04   7.7062e+02   5.3944e-01   1.7045e-02   2.0079e-02   3.3671e+00   5.6631e+00   1.0000e+00
   60  00:00:02   1.0997e+03      9         -1.5017e-04   6.6860e-04   7.7757e+02   6.8416e-01   2.8595e-02   2.3006e-02   2.7942e+00   5.2004e+00   1.0000e+00
   63  00:00:02   1.1039e+03     10  SN     -9.5077e-05   6.7969e-04   7.8056e+02   7.7830e-01   3.2608e-02   2.3836e-02   2.6063e+00   5.0309e+00   1.0000e+00
   65  00:00:02   1.1077e+03     11  HB     -7.0811e-05   6.8802e-04   7.8327e+02   8.8055e-01   3.5908e-02   2.4505e-02   2.4670e+00   4.9063e+00   1.0000e+00
   67  00:00:02   1.1117e+03     12  EP     -5.6648e-05   6.9554e-04   7.8606e+02   1.0000e+00   3.9079e-02   2.5140e-02   2.3497e+00   4.8029e+00   1.0000e+00
Backbone curve along branch point (BP) 24

 Run='bcssm-dof1.freq.bp2': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.1117e+03      1  EP      0.0000e+00   6.9552e-04   7.8606e+02   0.0000e+00   3.9079e-02   2.5140e-02   2.3497e+00   4.8028e+00   1.0000e+00
    5  00:00:00   1.1117e+03      2  EP      1.0000e+00   6.9554e-04   7.8606e+02  -5.6648e-05   3.9079e-02   2.5140e-02   2.3497e+00   4.8029e+00   1.0000e+00

 Run='bcssm-dof1.freq.bc2': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          1.18e-14  1.11e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.1117e+03      1  EP     -5.6648e-05   6.9554e-04   7.8606e+02   1.0000e+00   3.9079e-02   2.5140e-02   2.3497e+00   4.8029e+00   1.0000e+00
    6  00:00:00   1.1077e+03      2  HB     -7.0811e-05   6.8802e-04   7.8327e+02   8.8055e-01   3.5908e-02   2.4505e-02   2.4670e+00   4.9063e+00   1.0000e+00
    8  00:00:00   1.1039e+03      3  SN     -9.5077e-05   6.7969e-04   7.8056e+02   7.7830e-01   3.2608e-02   2.3836e-02   2.6063e+00   5.0309e+00   1.0000e+00
   10  00:00:00   1.0979e+03      4         -1.9176e-04   6.6303e-04   7.7631e+02   6.5126e-01   2.6754e-02   2.2615e-02   2.8837e+00   5.2814e+00   1.0000e+00
   15  00:00:01   1.0899e+03      5  SN     -7.0559e-04   6.2018e-04   7.7061e+02   5.3941e-01   1.7042e-02   2.0078e-02   3.3673e+00   5.6632e+00   1.0000e+00
   20  00:00:01   1.0884e+03      6         -9.6748e-04   6.0960e-04   7.6960e+02   5.2570e-01   1.5602e-02   1.9393e-02   3.5376e+00   5.7235e+00   1.0000e+00
   30  00:00:01   1.0884e+03      7         -9.8749e-04   6.1020e-04   7.6960e+02   5.2631e-01   1.5648e-02   1.9401e-02   3.5443e+00   5.7238e+00   1.0000e+00
   40  00:00:02   1.0884e+03      8         -1.0040e-03   6.1082e-04   7.6961e+02   5.2693e-01   1.5698e-02   1.9412e-02   3.5490e+00   5.7236e+00   1.0000e+00
   50  00:00:02   1.0887e+03      9         -1.1278e-03   6.1749e-04   7.6977e+02   5.3318e-01   1.6287e-02   1.9597e-02   3.5658e+00   5.7140e+00   1.0000e+00
   57  00:00:02   1.0963e+03     10  FP     -2.3159e-03   7.6867e-04   7.7514e+02   6.1295e-01   2.6688e-02   2.4173e-02   3.4006e+00   5.3702e+00   1.0000e+00
   60  00:00:02   1.1033e+03     11         -2.1429e-03   9.4913e-04   7.8011e+02   6.9349e-01   3.3132e-02   2.9273e-02   3.3545e+00   5.1949e+00   1.0000e+00
   69  00:00:03   1.1300e+03     12  EP     -1.6860e-03   1.5250e-03   7.9899e+02   1.0000e+00   5.0315e-02   4.6423e-02   3.3205e+00   5.0083e+00   1.0000e+00
Backbone curve along branch point (BP) 42

 Run='bcssm-dof1.freq.bp3': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.2075e+03      1  EP      0.0000e+00   3.1036e-03   8.5380e+02   0.0000e+00   4.7053e-04   9.8059e-02   3.4521e+00   4.7024e+00   1.0000e+00
    5  00:00:00   1.2075e+03      2  EP      1.0000e+00   3.1036e-03   8.5380e+02  -2.5295e-03   4.7053e-04   9.8059e-02   3.4521e+00   4.7024e+00   1.0000e+00

 Run='bcssm-dof1.freq.bc3': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          5.57e-13  1.21e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.2075e+03      1  EP     -2.5295e-03   3.1036e-03   8.5380e+02   1.0000e+00   4.7053e-04   9.8059e-02   3.4521e+00   4.7024e+00   1.0000e+00
   10  00:00:00   1.1722e+03      2         -2.7636e-03   2.5187e-03   8.2883e+02   7.7834e-01   4.9888e-04   7.8111e-02   3.4547e+00   4.7011e+00   1.0000e+00
   20  00:00:00   1.1163e+03      3         -3.2347e-03   1.4546e-03   7.8930e+02   4.2354e-01   6.4969e-04   4.3702e-02   3.4867e+00   4.6994e+00   1.0000e+00
   30  00:00:00   1.0890e+03      4         -3.5100e-03   4.6853e-04   7.7002e+02   1.3257e-01   6.2595e-04   1.3834e-02   3.5160e+00   4.7039e+00   1.0000e+00
   37  00:00:01   1.0858e+03      5  EP     -3.5461e-03   3.5462e-05   7.6777e+02   1.0000e-02   6.2161e-05   1.0443e-03   3.5220e+00   4.7062e+00   1.0000e+00

timings = 

  struct with fields:

    wa: 31.4584

We extract ridges of trenches of the FRS of $||w_\mathrm{B}||_{\mathcal{L}^2}$

startwb = tic
optdof = outdof(2);
S.extract_ridges_trenches('bcssm-dof2',resonant_modes,order,mFreq,parRange,outdof(2),optdof,{sol.p,sol.x});
timings.wb = toc(startwb)

startwb =

  uint64

   41464218996333

(near) outer resonance detected for the following combination of master eigenvalues
     0     0     1     1
     0     1     1     0
     1     0     0     1
     1     1     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     1
     0     1     1     0
     1     0     0     1
     1     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     0
     1     0     1     0
     2     0     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     0     2
     0     1     0     1
     0     2     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     0
     1     0     1     0
     2     0     0     0
     0     0     0     2
     0     1     0     1
     0     2     0     0

These are in resonance with the follwing eigenvalues of the slave subspace
   1.0e+03 *

  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0052 + 1.5311i
  -0.0052 + 1.5311i
  -0.0052 + 1.5311i
  -0.0052 - 1.5311i
  -0.0052 - 1.5311i
  -0.0052 - 1.5311i

sigma_out = 3
(near) inner resonance detected for the following combination of master eigenvalues
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0

These are in resonance with the follwing eigenvalues of the master subspace
   1.0e+02 *

  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i

sigma_in = 3
Due to (near) outer resonance, the exisitence of the manifold is questionable and the underlying computation may suffer.
Attempting manifold computation
Manifold computation time at order 2 = 00:00:00
Estimated memory usage at order  2 = 1.64E+00 MB
Manifold computation time at order 3 = 00:00:00
Estimated memory usage at order  3 = 3.53E+00 MB
Manifold computation time at order 4 = 00:00:00
Estimated memory usage at order  4 = 8.23E+00 MB
Manifold computation time at order 5 = 00:00:01
Estimated memory usage at order  5 = 1.56E+01 MB

Equation solved at initial point.

fsolve completed because the vector of function values at the initial point
is near zero as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


 Run='bcssm-dof2.freq.frc': Continue equilibria along primary branch.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          7.58e-14  1.08e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE           obj        d.obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.0799e+03      1  EP      2.1971e-04   0.0000e+00   7.6359e+02   0.0000e+00   5.6525e-03   1.9407e-02   5.7177e+00   6.1050e+00   1.0000e+00
   10  00:00:00   1.0709e+03      2          1.2451e-04   0.0000e+00   7.5722e+02   0.0000e+00   3.2006e-03   1.3569e-02   6.0791e+00   6.1532e+00   1.0000e+00
   20  00:00:00   1.0591e+03      3          6.9139e-05   0.0000e+00   7.4886e+02   0.0000e+00   1.7765e-03   8.8062e-03   6.1762e+00   6.1987e+00   1.0000e+00
   30  00:00:00   1.0461e+03      4          4.4459e-05   0.0000e+00   7.3962e+02   0.0000e+00   1.1422e-03   6.1231e-03   6.2149e+00   6.2245e+00   1.0000e+00
   40  00:00:01   1.0309e+03      5          3.1093e-05   0.0000e+00   7.2888e+02   0.0000e+00   7.9882e-04   4.4789e-03   6.2355e+00   6.2403e+00   1.0000e+00
   43  00:00:01   1.0260e+03      6  EP      2.8316e-05   0.0000e+00   7.2541e+02   0.0000e+00   7.2746e-04   4.1180e-03   6.2398e+00   6.2437e+00   1.0000e+00

 STEP      TIME        ||U||  LABEL  TYPE           obj        d.obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:01   1.0799e+03      7  EP      2.1971e-04   0.0000e+00   7.6359e+02   0.0000e+00   5.6525e-03   1.9407e-02   5.7177e+00   6.1050e+00   1.0000e+00
   10  00:00:01   1.0891e+03      8          6.8221e-04   0.0000e+00   7.7009e+02   0.0000e+00   1.7568e-02   2.5856e-02   4.4176e+00   6.0206e+00   1.0000e+00
   20  00:00:01   1.1120e+03      9          1.4873e-03   0.0000e+00   7.8625e+02   0.0000e+00   3.8789e-02   3.8407e-02   3.8956e+00   5.5869e+00   1.0000e+00
   30  00:00:02   1.1303e+03     10          1.9194e-03   0.0000e+00   7.9923e+02   0.0000e+00   5.0569e-02   4.6326e-02   3.2506e+00   4.9418e+00   1.0000e+00
   38  00:00:03   1.1303e+03     11  SN      1.9206e-03   0.0000e+00   7.9925e+02   0.0000e+00   5.0600e-02   4.6248e-02   3.2296e+00   4.9220e+00   1.0000e+00
   40  00:00:03   1.1303e+03     12          1.9207e-03   0.0000e+00   7.9925e+02   0.0000e+00   5.0603e-02   4.6231e-02   3.2255e+00   4.9182e+00   1.0000e+00
   49  00:00:03   1.1303e+03     13  BP      1.9210e-03   0.0000e+00   7.9923e+02   0.0000e+00   5.0610e-02   4.6144e-02   3.2076e+00   4.9015e+00   1.0000e+00
   50  00:00:03   1.1303e+03     14          1.9210e-03   0.0000e+00   7.9922e+02   0.0000e+00   5.0608e-02   4.6108e-02   3.2009e+00   4.8952e+00   1.0000e+00
   60  00:00:03   1.1291e+03     15          1.9027e-03   0.0000e+00   7.9838e+02   0.0000e+00   5.0095e-02   4.4793e-02   3.0584e+00   4.7653e+00   1.0000e+00
   70  00:00:04   1.1107e+03     16          1.5182e-03   0.0000e+00   7.8539e+02   0.0000e+00   3.9564e-02   2.6301e-02   2.4029e+00   4.5186e+00   1.0000e+00
   80  00:00:04   1.1105e+03     17          1.5067e-03   0.0000e+00   7.8524e+02   0.0000e+00   3.9254e-02   2.5432e-02   2.3778e+00   4.5801e+00   1.0000e+00
   83  00:00:05   1.1105e+03     18  SN      1.5062e-03   0.0000e+00   7.8524e+02   0.0000e+00   3.9243e-02   2.5397e-02   2.3767e+00   4.5838e+00   1.0000e+00
   90  00:00:05   1.1105e+03     19          1.5048e-03   0.0000e+00   7.8524e+02   0.0000e+00   3.9205e-02   2.5282e-02   2.3729e+00   4.5971e+00   1.0000e+00
  100  00:00:05   1.1107e+03     20          1.5013e-03   0.0000e+00   7.8533e+02   0.0000e+00   3.9113e-02   2.4994e-02   2.3618e+00   4.6469e+00   1.0000e+00
  101  00:00:05   1.1107e+03     21  HB      1.5008e-03   0.0000e+00   7.8537e+02   0.0000e+00   3.9101e-02   2.4955e-02   2.3598e+00   4.6588e+00   1.0000e+00
  104  00:00:05   1.1113e+03     22  BP      1.4993e-03   0.0000e+00   7.8576e+02   0.0000e+00   3.9069e-02   2.4947e-02   2.3506e+00   4.7510e+00   1.0000e+00
  106  00:00:06   1.1122e+03     23  BP      1.4997e-03   0.0000e+00   7.8644e+02   0.0000e+00   3.9092e-02   2.5497e-02   2.3520e+00   4.8607e+00   1.0000e+00
  109  00:00:06   1.1161e+03     24  HB      1.4304e-03   0.0000e+00   7.8915e+02   0.0000e+00   3.7319e-02   3.1193e-02   2.4732e+00   5.2751e+00   1.0000e+00
  110  00:00:06   1.1161e+03     25          1.4186e-03   0.0000e+00   7.8920e+02   0.0000e+00   3.7009e-02   3.1595e-02   2.4857e+00   5.2984e+00   1.0000e+00
  119  00:00:07   1.1162e+03     26  SN      1.3966e-03   0.0000e+00   7.8923e+02   0.0000e+00   3.6429e-02   3.2250e-02   2.5073e+00   5.3364e+00   1.0000e+00
  120  00:00:07   1.1162e+03     27          1.3949e-03   0.0000e+00   7.8923e+02   0.0000e+00   3.6384e-02   3.2297e-02   2.5089e+00   5.3391e+00   1.0000e+00
  130  00:00:07   1.1161e+03     28          1.3776e-03   0.0000e+00   7.8921e+02   0.0000e+00   3.5928e-02   3.2737e-02   2.5245e+00   5.3650e+00   1.0000e+00
  140  00:00:07   1.1155e+03     29          1.2740e-03   0.0000e+00   7.8872e+02   0.0000e+00   3.3198e-02   3.4664e-02   2.6027e+00   5.4826e+00   1.0000e+00
  150  00:00:08   1.1114e+03     30          7.7680e-04   0.0000e+00   7.8584e+02   0.0000e+00   2.0155e-02   3.9652e-02   2.8038e+00   5.7492e+00   1.0000e+00
  160  00:00:08   1.1114e+03     31  SN      7.6126e-04   0.0000e+00   7.8584e+02   0.0000e+00   1.9750e-02   3.9822e-02   2.8066e+00   5.7533e+00   1.0000e+00
  160  00:00:08   1.1114e+03     32          7.6074e-04   0.0000e+00   7.8584e+02   0.0000e+00   1.9736e-02   3.9828e-02   2.8067e+00   5.7534e+00   1.0000e+00
  170  00:00:09   1.1114e+03     33          7.5350e-04   0.0000e+00   7.8584e+02   0.0000e+00   1.9548e-02   3.9910e-02   2.8079e+00   5.7552e+00   1.0000e+00
  180  00:00:09   1.1114e+03     34          7.2604e-04   0.0000e+00   7.8586e+02   0.0000e+00   1.8833e-02   4.0231e-02   2.8121e+00   5.7616e+00   1.0000e+00
  190  00:00:09   1.1180e+03     35          4.0042e-04   0.0000e+00   7.9054e+02   0.0000e+00   1.0389e-02   4.7276e-02   2.7934e+00   5.7672e+00   1.0000e+00
  200  00:00:09   1.1525e+03     36          1.5571e-04   0.0000e+00   8.1491e+02   0.0000e+00   4.0653e-03   6.8451e-02   2.5674e+00   5.5307e+00   1.0000e+00
  210  00:00:10   1.1951e+03     37          5.1256e-05   0.0000e+00   8.4506e+02   0.0000e+00   1.3273e-03   9.1477e-02   2.3347e+00   5.0961e+00   1.0000e+00
  220  00:00:10   1.2046e+03     38          2.5795e-05   0.0000e+00   8.5175e+02   0.0000e+00   6.5268e-04   9.6618e-02   2.5374e+00   4.8898e+00   1.0000e+00
  230  00:00:10   1.2068e+03     39          1.8546e-05   0.0000e+00   8.5330e+02   0.0000e+00   4.7182e-04   9.7766e-02   2.9420e+00   4.7903e+00   1.0000e+00
  239  00:00:11   1.2074e+03     40  BP      1.7265e-05   0.0000e+00   8.5372e+02   0.0000e+00   4.5199e-04   9.8033e-02   3.2771e+00   4.7334e+00   1.0000e+00
  240  00:00:11   1.2074e+03     41          1.7335e-05   0.0000e+00   8.5377e+02   0.0000e+00   4.5757e-04   9.8055e-02   3.3545e+00   4.7201e+00   1.0000e+00
  246  00:00:11   1.2075e+03     42  SN      1.7966e-05   0.0000e+00   8.5381e+02   0.0000e+00   4.8224e-04   9.8048e-02   3.5119e+00   4.6908e+00   1.0000e+00
  250  00:00:11   1.2075e+03     43          1.8708e-05   0.0000e+00   8.5379e+02   0.0000e+00   5.0675e-04   9.8002e-02   3.6028e+00   4.6713e+00   1.0000e+00
  260  00:00:12   1.2072e+03     44          2.1350e-05   0.0000e+00   8.5358e+02   0.0000e+00   5.8631e-04   9.7754e-02   3.7739e+00   4.6243e+00   1.0000e+00
  270  00:00:12   1.2036e+03     45          3.5250e-05   0.0000e+00   8.5105e+02   0.0000e+00   9.7016e-04   9.5393e-02   4.0033e+00   4.4609e+00   1.0000e+00
  280  00:00:12   1.1613e+03     46          9.2153e-05   0.0000e+00   8.2116e+02   0.0000e+00   2.4521e-03   7.0616e-02   3.7555e+00   3.9119e+00   1.0000e+00
  289  00:00:13   1.1233e+03     47  BP      1.1279e-04   0.0000e+00   7.9429e+02   0.0000e+00   2.9433e-03   4.5225e-02   3.4867e+00   3.5942e+00   1.0000e+00
  290  00:00:13   1.1200e+03     48          1.1247e-04   0.0000e+00   7.9196e+02   0.0000e+00   2.9301e-03   4.2427e-02   3.4603e+00   3.5636e+00   1.0000e+00
  300  00:00:13   1.1047e+03     49          8.5101e-05   0.0000e+00   7.8114e+02   0.0000e+00   2.1953e-03   2.0999e-02   3.2878e+00   3.3444e+00   1.0000e+00
  310  00:00:14   1.1046e+03     50          8.1890e-05   0.0000e+00   7.8109e+02   0.0000e+00   2.1117e-03   1.9733e-02   3.2796e+00   3.3320e+00   1.0000e+00
  313  00:00:14   1.1046e+03     51  SN      8.1781e-05   0.0000e+00   7.8109e+02   0.0000e+00   2.1088e-03   1.9692e-02   3.2794e+00   3.3316e+00   1.0000e+00
  320  00:00:14   1.1046e+03     52          8.1497e-05   0.0000e+00   7.8109e+02   0.0000e+00   2.1014e-03   1.9584e-02   3.2787e+00   3.3305e+00   1.0000e+00
  330  00:00:14   1.1047e+03     53          8.0610e-05   0.0000e+00   7.8110e+02   0.0000e+00   2.0783e-03   1.9250e-02   3.2766e+00   3.3273e+00   1.0000e+00
  340  00:00:15   1.1060e+03     54          6.7956e-05   0.0000e+00   7.8201e+02   0.0000e+00   1.7500e-03   1.4972e-02   3.2500e+00   3.2856e+00   1.0000e+00
  350  00:00:15   1.1140e+03     55          4.6826e-05   0.0000e+00   7.8771e+02   0.0000e+00   1.2044e-03   9.2226e-03   3.2140e+00   3.2301e+00   1.0000e+00
  360  00:00:15   1.1263e+03     56          3.3521e-05   0.0000e+00   7.9642e+02   0.0000e+00   8.6180e-04   6.2053e-03   3.1931e+00   3.2011e+00   1.0000e+00
  370  00:00:16   1.1417e+03     57          2.4972e-05   0.0000e+00   8.0732e+02   0.0000e+00   6.4186e-04   4.4530e-03   3.1799e+00   3.1843e+00   1.0000e+00
  380  00:00:16   1.1599e+03     58          1.9251e-05   0.0000e+00   8.2018e+02   0.0000e+00   4.9475e-04   3.3510e-03   3.1711e+00   3.1737e+00   1.0000e+00
  390  00:00:16   1.1808e+03     59          1.5258e-05   0.0000e+00   8.3492e+02   0.0000e+00   3.9212e-04   2.6127e-03   3.1650e+00   3.1666e+00   1.0000e+00
  400  00:00:16   1.2042e+03     60          1.2375e-05   0.0000e+00   8.5150e+02   0.0000e+00   3.1802e-04   2.0944e-03   3.1606e+00   3.1616e+00   1.0000e+00
  410  00:00:17   1.2305e+03     61          1.0216e-05   0.0000e+00   8.7006e+02   0.0000e+00   2.6251e-04   1.7140e-03   3.1572e+00   3.1580e+00   1.0000e+00
  414  00:00:17   1.2419e+03     62  EP      9.4957e-06   0.0000e+00   8.7813e+02   0.0000e+00   2.4401e-04   1.5886e-03   3.1561e+00   3.1568e+00   1.0000e+00
Backbone curve along branch point (BP) 13

 Run='bcssm-dof2.freq.bp1': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.1303e+03      1  EP      0.0000e+00   1.9210e-03   7.9923e+02   0.0000e+00   5.0610e-02   4.6144e-02   3.2076e+00   4.9015e+00   1.0000e+00
    5  00:00:00   1.1303e+03      2  EP      1.0000e+00   1.9210e-03   7.9923e+02  -1.7975e-03   5.0610e-02   4.6144e-02   3.2076e+00   4.9015e+00   1.0000e+00

 Run='bcssm-dof2.freq.bc1': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          3.99e-12  1.13e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.1303e+03      1  EP     -1.7975e-03   1.9210e-03   7.9923e+02   1.0000e+00   5.0610e-02   4.6144e-02   3.2076e+00   4.9015e+00   1.0000e+00
   10  00:00:00   1.1082e+03      2         -2.1802e-03   1.4242e-03   7.8361e+02   7.4480e-01   3.7066e-02   3.1781e-02   3.1588e+00   4.9769e+00   1.0000e+00
   13  00:00:00   1.0994e+03      3  SN     -3.1020e-03   1.1531e-03   7.7737e+02   6.3644e-01   2.9860e-02   2.5100e-02   3.1664e+00   5.1499e+00   1.0000e+00
   16  00:00:00   1.0916e+03      4  FP     -6.2916e-03   7.9755e-04   7.7187e+02   5.5898e-01   2.0555e-02   2.0860e-02   3.3705e+00   5.5541e+00   1.0000e+00
   20  00:00:00   1.0856e+03      5         -2.1401e-03   3.8070e-04   7.6759e+02   4.5357e-01   9.7750e-03   1.7149e-02   3.6765e+00   5.8355e+00   1.0000e+00
   26  00:00:01   1.0808e+03      6  FP     -5.6664e-04   1.1924e-04   7.6422e+02   1.9432e-01   3.0579e-03   7.4966e-03   4.5499e+00   5.9081e+00   1.0000e+00
   30  00:00:01   1.0800e+03      7         -6.5010e-04   1.8992e-05   7.6361e+02   2.9096e-02   4.8700e-04   1.1375e-03   4.7096e+00   5.8996e+00   1.0000e+00
   34  00:00:01   1.0799e+03      8  EP     -6.5358e-04   6.5395e-06   7.6359e+02   1.0001e-02   1.6769e-04   3.9123e-04   4.7115e+00   5.8992e+00   1.0000e+00
Backbone curve along branch point (BP) 22

 Run='bcssm-dof2.freq.bp2': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.1113e+03      1  EP      0.0000e+00   1.4993e-03   7.8576e+02   0.0000e+00   3.9069e-02   2.4947e-02   2.3506e+00   4.7510e+00   1.0000e+00
    1  00:00:00   1.1113e+03      2  BP      3.8006e-08   1.4993e-03   7.8576e+02  -3.2826e-11   3.9069e-02   2.4947e-02   2.3506e+00   4.7510e+00   1.0000e+00
    5  00:00:00   1.1113e+03      3  EP      1.0000e+00   1.4993e-03   7.8576e+02  -8.6372e-04   3.9069e-02   2.4947e-02   2.3506e+00   4.7510e+00   1.0000e+00

 Run='bcssm-dof2.freq.bc2': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          7.60e-14  1.11e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.1113e+03      1  EP     -8.6372e-04   1.4993e-03   7.8576e+02   1.0000e+00   3.9069e-02   2.4947e-02   2.3506e+00   4.7510e+00   1.0000e+00
   10  00:00:00   1.1113e+03      2         -8.9097e-04   1.4957e-03   7.8581e+02   9.9592e-01   3.8976e-02   2.5004e-02   2.3533e+00   4.7786e+00   1.0000e+00
   16  00:00:00   1.1122e+03      3  EP     -9.7179e-04   1.4997e-03   7.8644e+02   1.0000e+00   3.9092e-02   2.5498e-02   2.3520e+00   4.8606e+00   1.0000e+00
Backbone curve along branch point (BP) 23

 Run='bcssm-dof2.freq.bp3': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.1122e+03      1  EP      0.0000e+00   1.4997e-03   7.8644e+02   0.0000e+00   3.9092e-02   2.5497e-02   2.3520e+00   4.8607e+00   1.0000e+00
    5  00:00:00   1.1122e+03      2  EP      1.0000e+00   1.4997e-03   7.8644e+02  -9.7179e-04   3.9092e-02   2.5498e-02   2.3520e+00   4.8606e+00   1.0000e+00

 Run='bcssm-dof2.freq.bc3': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          6.22e-14  1.11e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.1122e+03      1  EP     -9.7179e-04   1.4997e-03   7.8644e+02   1.0000e+00   3.9092e-02   2.5498e-02   2.3520e+00   4.8606e+00   1.0000e+00
   10  00:00:00   1.1113e+03      2  EP     -8.6372e-04   1.4993e-03   7.8576e+02   1.0000e+00   3.9069e-02   2.4947e-02   2.3506e+00   4.7510e+00   1.0000e+00
Backbone curve along branch point (BP) 40

 Run='bcssm-dof2.freq.bp4': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.2074e+03      1  EP      0.0000e+00   1.7265e-05   8.5372e+02   0.0000e+00   4.5199e-04   9.8033e-02   3.2771e+00   4.7334e+00   1.0000e+00
    5  00:00:00   1.2074e+03      2  EP      1.0000e+00   1.7265e-05   8.5372e+02   2.0763e-06   4.5199e-04   9.8033e-02   3.2771e+00   4.7334e+00   1.0000e+00

 Run='bcssm-dof2.freq.bc4': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          7.06e-14  1.21e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.2074e+03      1  EP      2.0763e-06   1.7265e-05   8.5372e+02   1.0000e+00   4.5199e-04   9.8033e-02   3.2771e+00   4.7334e+00   1.0000e+00
   10  00:00:00   1.1720e+03      2          8.8806e-06   1.8438e-05   8.2874e+02   7.7849e-01   4.8010e-04   7.8093e-02   3.2757e+00   4.7377e+00   1.0000e+00
   20  00:00:00   1.1169e+03      3          2.5416e-05   2.4275e-05   7.8975e+02   4.3004e-01   6.2730e-04   4.4294e-02   3.3385e+00   4.7608e+00   1.0000e+00
   30  00:00:00   1.0897e+03      4         -9.8239e-05   2.4789e-05   7.7051e+02   1.4065e-01   6.3881e-04   1.4450e-02   3.5389e+00   4.5352e+00   1.0000e+00
   40  00:00:01   1.0895e+03      5         -1.1692e-04   2.4034e-05   7.7035e+02   1.3355e-01   6.1963e-04   1.3402e-02   3.5377e+00   4.4333e+00   1.0000e+00
   50  00:00:01   1.0895e+03      6         -1.2171e-04   2.3993e-05   7.7036e+02   1.3320e-01   6.1868e-04   1.3203e-02   3.5363e+00   4.3929e+00   1.0000e+00
   60  00:00:02   1.0898e+03      7         -1.3019e-04   2.4798e-05   7.7059e+02   1.3950e-01   6.3978e-04   1.3167e-02   3.5311e+00   4.2707e+00   1.0000e+00
   61  00:00:02   1.0900e+03      8  SN     -1.3125e-04   2.5261e-05   7.7070e+02   1.4304e-01   6.5182e-04   1.3290e-02   3.5298e+00   4.2387e+00   1.0000e+00
   70  00:00:02   1.1019e+03      9         -1.0735e-04   6.3631e-05   7.7918e+02   4.6269e-01   1.6488e-03   2.7879e-02   3.5270e+00   3.7584e+00   1.0000e+00
   78  00:00:02   1.1233e+03     10  EP     -7.8264e-05   1.1279e-04   7.9429e+02   1.0000e+00   2.9433e-03   4.5225e-02   3.4867e+00   3.5942e+00   1.0000e+00
Backbone curve along branch point (BP) 47

 Run='bcssm-dof2.freq.bp5': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.1233e+03      1  EP      0.0000e+00   1.1279e-04   7.9429e+02   0.0000e+00   2.9433e-03   4.5225e-02   3.4867e+00   3.5942e+00   1.0000e+00
    5  00:00:00   1.1233e+03      2  EP      1.0000e+00   1.1279e-04   7.9429e+02  -7.8264e-05   2.9433e-03   4.5225e-02   3.4867e+00   3.5942e+00   1.0000e+00

 Run='bcssm-dof2.freq.bc5': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          4.33e-14  1.12e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.1233e+03      1  EP     -7.8264e-05   1.1279e-04   7.9429e+02   1.0000e+00   2.9433e-03   4.5225e-02   3.4867e+00   3.5942e+00   1.0000e+00
   10  00:00:00   1.1032e+03      2         -1.0517e-04   6.6984e-05   7.8008e+02   4.9425e-01   1.7364e-03   2.9144e-02   3.5262e+00   3.7436e+00   1.0000e+00
   16  00:00:00   1.0903e+03      3  FP     -1.3239e-04   2.6466e-05   7.7095e+02   1.5218e-01   6.8308e-04   1.3670e-02   3.5273e+00   4.1769e+00   1.0000e+00
   16  00:00:00   1.0900e+03      4  SN     -1.3124e-04   2.5254e-05   7.7069e+02   1.4299e-01   6.5163e-04   1.3288e-02   3.5298e+00   4.2392e+00   1.0000e+00
   20  00:00:01   1.0895e+03      5         -1.2139e-04   2.3991e-05   7.7036e+02   1.3319e-01   6.1862e-04   1.3214e-02   3.5364e+00   4.3960e+00   1.0000e+00
   30  00:00:01   1.0895e+03      6         -1.1594e-04   2.4057e-05   7.7035e+02   1.3374e-01   6.2019e-04   1.3449e-02   3.5379e+00   4.4404e+00   1.0000e+00
   40  00:00:01   1.0895e+03      7         -1.0818e-04   2.4326e-05   7.7040e+02   1.3615e-01   6.2700e-04   1.3857e-02   3.5389e+00   4.4884e+00   1.0000e+00
   50  00:00:01   1.0920e+03      8         -3.6835e-05   2.7654e-05   7.7216e+02   1.8512e-01   7.1240e-04   1.9296e-02   3.5158e+00   4.6917e+00   1.0000e+00
   60  00:00:02   1.1121e+03      9          2.6475e-05   2.5226e-05   7.8638e+02   3.9350e-01   6.5144e-04   4.0611e-02   3.3566e+00   4.7636e+00   1.0000e+00
   70  00:00:02   1.1441e+03     10          1.6111e-05   2.0499e-05   8.0899e+02   6.1095e-01   5.3169e-04   6.2178e-02   3.2884e+00   4.7462e+00   1.0000e+00
   80  00:00:02   1.2011e+03     11          3.2167e-06   1.7376e-05   8.4928e+02   9.5795e-01   4.5443e-04   9.4349e-02   3.2762e+00   4.7337e+00   1.0000e+00
   81  00:00:02   1.2074e+03     12  EP      2.0763e-06   1.7265e-05   8.5372e+02   1.0000e+00   4.5199e-04   9.8033e-02   3.2771e+00   4.7334e+00   1.0000e+00

timings = 

  struct with fields:

    wa: 31.4584
    wb: 31.3789

We extract ridges of trenches of the FRS of $||E_k||_{\mathcal{L}^2}$

startek = tic
optdof = n+1:2*n;
set(S.contOptions, 'PtMX', 450, 'MaxRes', 0.5);
set(S.FRCOptions,'DBCobjweight',M/2);
S.extract_ridges_trenches('bcssm-Et',resonant_modes,order,mFreq,parRange,outdof,optdof,{sol.p,sol.x});
timings.ek = toc(startek)

startek =

  uint64

   41496275483000

(near) outer resonance detected for the following combination of master eigenvalues
     0     0     1     1
     0     1     1     0
     1     0     0     1
     1     1     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     1
     0     1     1     0
     1     0     0     1
     1     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     0
     1     0     1     0
     2     0     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     0     2
     0     1     0     1
     0     2     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     0
     1     0     1     0
     2     0     0     0
     0     0     0     2
     0     1     0     1
     0     2     0     0

These are in resonance with the follwing eigenvalues of the slave subspace
   1.0e+03 *

  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 + 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0007 - 0.3067i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 + 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0035 - 1.2188i
  -0.0052 + 1.5311i
  -0.0052 + 1.5311i
  -0.0052 + 1.5311i
  -0.0052 - 1.5311i
  -0.0052 - 1.5311i
  -0.0052 - 1.5311i

sigma_out = 3
(near) inner resonance detected for the following combination of master eigenvalues
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0
     0     0     2     1
     0     1     2     0
     1     0     1     1
     1     1     1     0
     2     0     0     1
     2     1     0     0
     0     0     1     2
     0     1     1     1
     0     2     1     0
     1     0     0     2
     1     1     0     1
     1     2     0     0

These are in resonance with the follwing eigenvalues of the master subspace
   1.0e+02 *

  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 + 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0167 - 7.6359i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 + 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i
  -0.0168 - 7.6775i

sigma_in = 3
Due to (near) outer resonance, the exisitence of the manifold is questionable and the underlying computation may suffer.
Attempting manifold computation
Manifold computation time at order 2 = 00:00:00
Estimated memory usage at order  2 = 1.64E+00 MB
Manifold computation time at order 3 = 00:00:00
Estimated memory usage at order  3 = 3.53E+00 MB
Manifold computation time at order 4 = 00:00:00
Estimated memory usage at order  4 = 8.23E+00 MB
Manifold computation time at order 5 = 00:00:01
Estimated memory usage at order  5 = 1.56E+01 MB

Equation solved at initial point.

fsolve completed because the vector of function values at the initial point
is near zero as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


 Run='bcssm-Et.freq.frc': Continue equilibria along primary branch.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          7.58e-14  1.08e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE           obj        d.obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.0799e+03      1  EP      1.0363e+00   0.0000e+00   7.6359e+02   0.0000e+00   5.6525e-03   1.9407e-02   5.7177e+00   6.1050e+00   1.0000e+00
   10  00:00:00   1.0648e+03      2          5.6008e-01   0.0000e+00   7.5285e+02   0.0000e+00   2.2900e-03   1.0697e-02   6.1435e+00   6.1806e+00   1.0000e+00
   20  00:00:01   1.0337e+03      3          2.4524e-01   0.0000e+00   7.3089e+02   0.0000e+00   8.4665e-04   4.7169e-03   6.2326e+00   6.2380e+00   1.0000e+00
   22  00:00:02   1.0260e+03      4  EP      2.1399e-01   0.0000e+00   7.2541e+02   0.0000e+00   7.2746e-04   4.1180e-03   6.2398e+00   6.2437e+00   1.0000e+00

 STEP      TIME        ||U||  LABEL  TYPE           obj        d.obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:02   1.0799e+03      5  EP      1.0363e+00   0.0000e+00   7.6359e+02   0.0000e+00   5.6525e-03   1.9407e-02   5.7177e+00   6.1050e+00   1.0000e+00
   10  00:00:02   1.0915e+03      6          1.7496e+00   0.0000e+00   7.7175e+02   0.0000e+00   2.0607e-02   2.7223e-02   4.3290e+00   5.9788e+00   1.0000e+00
   20  00:00:04   1.1301e+03      7          3.5472e+00   0.0000e+00   7.9911e+02   0.0000e+00   5.0428e-02   4.6417e-02   3.2964e+00   4.9853e+00   1.0000e+00
   23  00:00:05   1.1303e+03      8  BP      3.5495e+00   0.0000e+00   7.9922e+02   0.0000e+00   5.0547e-02   4.6355e-02   3.2606e+00   4.9512e+00   1.0000e+00
   23  00:00:05   1.1303e+03      9  FP      3.5495e+00   0.0000e+00   7.9922e+02   0.0000e+00   5.0547e-02   4.6355e-02   3.2606e+00   4.9512e+00   1.0000e+00
   30  00:00:06   1.1303e+03     10          3.5481e+00   0.0000e+00   7.9925e+02   0.0000e+00   5.0596e-02   4.6262e-02   3.2328e+00   4.9251e+00   1.0000e+00
   32  00:00:06   1.1303e+03     11  SN      3.5478e+00   0.0000e+00   7.9925e+02   0.0000e+00   5.0600e-02   4.6248e-02   3.2296e+00   4.9220e+00   1.0000e+00
   40  00:00:06   1.1303e+03     12          3.5454e+00   0.0000e+00   7.9924e+02   0.0000e+00   5.0609e-02   4.6171e-02   3.2128e+00   4.9063e+00   1.0000e+00
   50  00:00:07   1.1301e+03     13          3.5304e+00   0.0000e+00   7.9909e+02   0.0000e+00   5.0550e-02   4.5819e-02   3.1580e+00   4.8554e+00   1.0000e+00
   60  00:00:08   1.1110e+03     14          2.4658e+00   0.0000e+00   7.8557e+02   0.0000e+00   3.9780e-02   2.6854e-02   2.4177e+00   4.4944e+00   1.0000e+00
   70  00:00:10   1.1105e+03     15          2.4035e+00   0.0000e+00   7.8524e+02   0.0000e+00   3.9260e-02   2.5449e-02   2.3783e+00   4.5784e+00   1.0000e+00
   74  00:00:10   1.1105e+03     16  SN      2.4013e+00   0.0000e+00   7.8524e+02   0.0000e+00   3.9243e-02   2.5397e-02   2.3767e+00   4.5838e+00   1.0000e+00
   80  00:00:11   1.1105e+03     17          2.3970e+00   0.0000e+00   7.8524e+02   0.0000e+00   3.9209e-02   2.5294e-02   2.3733e+00   4.5956e+00   1.0000e+00
   90  00:00:11   1.1106e+03     18          2.3863e+00   0.0000e+00   7.8531e+02   0.0000e+00   3.9125e-02   2.5031e-02   2.3635e+00   4.6380e+00   1.0000e+00
   92  00:00:12   1.1107e+03     19  HB      2.3832e+00   0.0000e+00   7.8537e+02   0.0000e+00   3.9101e-02   2.4955e-02   2.3598e+00   4.6588e+00   1.0000e+00
   94  00:00:12   1.1110e+03     20  FP      2.3806e+00   0.0000e+00   7.8554e+02   0.0000e+00   3.9072e-02   2.4889e-02   2.3537e+00   4.7066e+00   1.0000e+00
   94  00:00:12   1.1110e+03     21  BP      2.3806e+00   0.0000e+00   7.8555e+02   0.0000e+00   3.9072e-02   2.4889e-02   2.3537e+00   4.7067e+00   1.0000e+00
  100  00:00:14   1.1160e+03     22          2.5074e+00   0.0000e+00   7.8913e+02   0.0000e+00   3.7415e-02   3.1058e-02   2.4691e+00   5.2673e+00   1.0000e+00
  101  00:00:14   1.1161e+03     23  HB      2.5082e+00   0.0000e+00   7.8915e+02   0.0000e+00   3.7319e-02   3.1193e-02   2.4732e+00   5.2751e+00   1.0000e+00
  104  00:00:15   1.1162e+03     24  FP      2.5101e+00   0.0000e+00   7.8922e+02   0.0000e+00   3.6718e-02   3.1938e-02   2.4968e+00   5.3182e+00   1.0000e+00
  104  00:00:15   1.1162e+03     25  BP      2.5101e+00   0.0000e+00   7.8922e+02   0.0000e+00   3.6718e-02   3.1938e-02   2.4968e+00   5.3182e+00   1.0000e+00
  110  00:00:15   1.1162e+03     26          2.5097e+00   0.0000e+00   7.8923e+02   0.0000e+00   3.6429e-02   3.2250e-02   2.5073e+00   5.3364e+00   1.0000e+00
  111  00:00:16   1.1162e+03     27  SN      2.5097e+00   0.0000e+00   7.8923e+02   0.0000e+00   3.6429e-02   3.2250e-02   2.5073e+00   5.3364e+00   1.0000e+00
  120  00:00:16   1.1162e+03     28          2.5081e+00   0.0000e+00   7.8922e+02   0.0000e+00   3.6011e-02   3.2661e-02   2.5218e+00   5.3605e+00   1.0000e+00
  130  00:00:17   1.1158e+03     29          2.4907e+00   0.0000e+00   7.8895e+02   0.0000e+00   3.4179e-02   3.4076e-02   2.5770e+00   5.4457e+00   1.0000e+00
  140  00:00:20   1.1114e+03     30          2.2979e+00   0.0000e+00   7.8584e+02   0.0000e+00   2.0228e-02   3.9622e-02   2.8033e+00   5.7485e+00   1.0000e+00
  150  00:00:21   1.1114e+03     31  SN      2.2962e+00   0.0000e+00   7.8584e+02   0.0000e+00   1.9750e-02   3.9822e-02   2.8066e+00   5.7533e+00   1.0000e+00
  150  00:00:21   1.1114e+03     32          2.2962e+00   0.0000e+00   7.8584e+02   0.0000e+00   1.9750e-02   3.9823e-02   2.8066e+00   5.7533e+00   1.0000e+00
  160  00:00:21   1.1114e+03     33          2.2958e+00   0.0000e+00   7.8584e+02   0.0000e+00   1.9566e-02   3.9902e-02   2.8078e+00   5.7550e+00   1.0000e+00
  170  00:00:22   1.1114e+03     34          2.2950e+00   0.0000e+00   7.8585e+02   0.0000e+00   1.8972e-02   4.0167e-02   2.8114e+00   5.7604e+00   1.0000e+00
  171  00:00:22   1.1114e+03     35  BP      2.2950e+00   0.0000e+00   7.8586e+02   0.0000e+00   1.8892e-02   4.0203e-02   2.8118e+00   5.7611e+00   1.0000e+00
  171  00:00:22   1.1114e+03     36  FP      2.2950e+00   0.0000e+00   7.8586e+02   0.0000e+00   1.8892e-02   4.0204e-02   2.8118e+00   5.7611e+00   1.0000e+00
  180  00:00:23   1.1203e+03     37          2.5847e+00   0.0000e+00   7.9216e+02   0.0000e+00   9.3938e-03   4.8945e-02   2.7783e+00   5.7544e+00   1.0000e+00
  190  00:00:24   1.1703e+03     38          4.1136e+00   0.0000e+00   8.2749e+02   0.0000e+00   2.7997e-03   7.8125e-02   2.4548e+00   5.3832e+00   1.0000e+00
  200  00:00:25   1.2046e+03     39          5.1226e+00   0.0000e+00   8.5178e+02   0.0000e+00   6.4851e-04   9.6644e-02   2.5418e+00   4.8881e+00   1.0000e+00
  210  00:00:26   1.2074e+03     40          5.1991e+00   0.0000e+00   8.5375e+02   0.0000e+00   4.5576e-04   9.8050e-02   3.3346e+00   4.7236e+00   1.0000e+00
  213  00:00:26   1.2075e+03     41  BP      5.1997e+00   0.0000e+00   8.5379e+02   0.0000e+00   4.6574e-04   9.8061e-02   3.4218e+00   4.7081e+00   1.0000e+00
  213  00:00:26   1.2075e+03     42  FP      5.1997e+00   0.0000e+00   8.5379e+02   0.0000e+00   4.6574e-04   9.8061e-02   3.4218e+00   4.7081e+00   1.0000e+00
  216  00:00:27   1.2075e+03     43  SN      5.1990e+00   0.0000e+00   8.5381e+02   0.0000e+00   4.8224e-04   9.8048e-02   3.5119e+00   4.6908e+00   1.0000e+00
  220  00:00:27   1.2075e+03     44          5.1967e+00   0.0000e+00   8.5379e+02   0.0000e+00   5.0462e-04   9.8007e-02   3.5961e+00   4.6729e+00   1.0000e+00
  230  00:00:28   1.2072e+03     45          5.1842e+00   0.0000e+00   8.5360e+02   0.0000e+00   5.8070e-04   9.7775e-02   3.7652e+00   4.6272e+00   1.0000e+00
  240  00:00:29   1.1964e+03     46          4.8166e+00   0.0000e+00   8.4599e+02   0.0000e+00   1.3814e-03   9.1029e-02   3.9999e+00   4.3065e+00   1.0000e+00
  250  00:00:29   1.1465e+03     47          3.2154e+00   0.0000e+00   8.1065e+02   0.0000e+00   2.7356e-03   6.1556e-02   3.6537e+00   3.7876e+00   1.0000e+00
  260  00:00:30   1.1049e+03     48          1.1424e+00   0.0000e+00   7.8128e+02   0.0000e+00   2.2666e-03   2.2141e-02   3.2954e+00   3.3556e+00   1.0000e+00
  270  00:00:32   1.1046e+03     49          1.0177e+00   0.0000e+00   7.8109e+02   0.0000e+00   2.1112e-03   1.9726e-02   3.2796e+00   3.3319e+00   1.0000e+00
  271  00:00:32   1.1046e+03     50  SN      1.0159e+00   0.0000e+00   7.8109e+02   0.0000e+00   2.1088e-03   1.9692e-02   3.2794e+00   3.3316e+00   1.0000e+00
  280  00:00:32   1.1047e+03     51          9.9165e-01   0.0000e+00   7.8110e+02   0.0000e+00   2.0764e-03   1.9223e-02   3.2764e+00   3.3270e+00   1.0000e+00
  290  00:00:33   1.1048e+03     52          9.1522e-01   0.0000e+00   7.8123e+02   0.0000e+00   1.9695e-03   1.7741e-02   3.2671e+00   3.3125e+00   1.0000e+00
  300  00:00:34   1.1173e+03     53          4.1974e-01   0.0000e+00   7.9005e+02   0.0000e+00   1.0850e-03   8.1271e-03   3.2066e+00   3.2195e+00   1.0000e+00
  310  00:00:35   1.1567e+03     54          1.8118e-01   0.0000e+00   8.1792e+02   0.0000e+00   5.1544e-04   3.5028e-03   3.1723e+00   3.1751e+00   1.0000e+00
  320  00:00:36   1.2067e+03     55          1.0614e-01   0.0000e+00   8.5328e+02   0.0000e+00   3.1170e-04   2.0508e-03   3.1602e+00   3.1612e+00   1.0000e+00
  328  00:00:36   1.2419e+03     56  EP      8.2243e-02   0.0000e+00   8.7813e+02   0.0000e+00   2.4401e-04   1.5886e-03   3.1561e+00   3.1568e+00   1.0000e+00
Backbone curve along branch point (BP) 8

 Run='bcssm-Et.freq.bp1': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.1303e+03      1  EP      0.0000e+00   3.5495e+00   7.9922e+02   0.0000e+00   5.0547e-02   4.6355e-02   3.2606e+00   4.9512e+00   1.0000e+00
    9  00:00:00   1.1308e+03      2  EP      1.0000e+00   3.5495e+00   7.9922e+02  -3.8325e+00   5.0547e-02   4.6355e-02   3.2606e+00   4.9512e+00   1.0000e+00

 Run='bcssm-Et.freq.bc1': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          5.99e-10  1.13e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.1308e+03      1  EP     -3.8325e+00   3.5495e+00   7.9922e+02   1.0000e+00   5.0547e-02   4.6355e-02   3.2606e+00   4.9512e+00   1.0000e+00
   10  00:00:00   1.1107e+03      2         -4.2715e+00   2.6180e+00   7.8492e+02   7.6791e-01   3.8281e-02   3.3576e-02   3.2431e+00   5.0289e+00   1.0000e+00
   20  00:00:01   1.0999e+03      3         -5.4929e+00   1.9640e+00   7.7680e+02   6.2855e-01   2.9078e-02   2.4992e-02   3.2445e+00   5.2164e+00   1.0000e+00
   30  00:00:02   1.0966e+03      4         -7.4777e+00   1.6336e+00   7.7324e+02   5.7663e-01   2.3328e-02   2.1801e-02   3.3189e+00   5.4445e+00   1.0000e+00
   34  00:00:02   1.0958e+03      5  FP     -7.7467e+00   1.5441e+00   7.7232e+02   5.6494e-01   2.1522e-02   2.1167e-02   3.3560e+00   5.5181e+00   1.0000e+00
   40  00:00:03   1.0953e+03      6         -7.6875e+00   1.5063e+00   7.7193e+02   5.6004e-01   2.0727e-02   2.0918e-02   3.3730e+00   5.5488e+00   1.0000e+00
   50  00:00:03   1.0948e+03      7         -7.5251e+00   1.4716e+00   7.7159e+02   5.5548e-01   1.9984e-02   2.0696e-02   3.3888e+00   5.5764e+00   1.0000e+00
   60  00:00:04   1.0930e+03      8         -6.6682e+00   1.3817e+00   7.7073e+02   5.4289e-01   1.8002e-02   2.0142e-02   3.4291e+00   5.6439e+00   1.0000e+00
   70  00:00:05   1.0881e+03      9         -2.8434e+00   1.1404e+00   7.6911e+02   4.9286e-01   1.1172e-02   1.9270e-02   3.3873e+00   5.7857e+00   1.0000e+00
   80  00:00:06   1.0954e+03     10         -2.3416e+00   1.5644e+00   7.7445e+02   6.6362e-01   1.3951e-02   2.7081e-02   2.9944e+00   5.7510e+00   1.0000e+00
   87  00:00:07   1.1115e+03     11  EP     -2.0121e+00   2.2950e+00   7.8586e+02   1.0000e+00   1.8892e-02   4.0203e-02   2.8118e+00   5.7611e+00   1.0000e+00
Backbone curve along branch point (BP) 21

 Run='bcssm-Et.freq.bp2': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.1110e+03      1  EP      0.0000e+00   2.3806e+00   7.8555e+02   0.0000e+00   3.9072e-02   2.4889e-02   2.3537e+00   4.7067e+00   1.0000e+00
    1  00:00:00   1.1110e+03      2  BP      7.4383e-09   2.3806e+00   7.8555e+02  -8.1696e-09   3.9072e-02   2.4889e-02   2.3537e+00   4.7067e+00   1.0000e+00
    7  00:00:00   1.1110e+03      3  EP      1.0000e+00   2.3806e+00   7.8555e+02  -1.0983e+00   3.9072e-02   2.4889e-02   2.3537e+00   4.7068e+00   1.0000e+00

 Run='bcssm-Et.freq.bc2': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          1.90e-13  1.11e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.1110e+03      1  EP     -1.0983e+00   2.3806e+00   7.8555e+02   1.0000e+00   3.9072e-02   2.4889e-02   2.3537e+00   4.7068e+00   1.0000e+00
    9  00:00:01   1.1076e+03      2  HB     -1.4747e+00   2.2228e+00   7.8317e+02   8.7401e-01   3.5639e-02   2.4564e-02   2.4758e+00   4.9354e+00   1.0000e+00
   10  00:00:01   1.1073e+03      3         -1.5710e+00   2.2008e+00   7.8289e+02   8.5955e-01   3.5053e-02   2.4658e-02   2.4964e+00   4.9854e+00   1.0000e+00
   20  00:00:01   1.1074e+03      4         -1.9043e+00   2.1869e+00   7.8298e+02   8.5047e-01   3.3858e-02   2.5793e-02   2.5376e+00   5.1460e+00   1.0000e+00
   30  00:00:02   1.1105e+03      5         -2.1442e+00   2.2962e+00   7.8515e+02   9.0366e-01   3.4452e-02   2.8358e-02   2.5302e+00   5.2582e+00   1.0000e+00
   34  00:00:03   1.1163e+03      6  EP     -2.2754e+00   2.5101e+00   7.8922e+02   1.0000e+00   3.6718e-02   3.1938e-02   2.4968e+00   5.3182e+00   1.0000e+00
Backbone curve along branch point (BP) 25

 Run='bcssm-Et.freq.bp3': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.1162e+03      1  EP      0.0000e+00   2.5101e+00   7.8922e+02   0.0000e+00   3.6718e-02   3.1938e-02   2.4968e+00   5.3182e+00   1.0000e+00
    8  00:00:00   1.1163e+03      2  EP      1.0000e+00   2.5101e+00   7.8922e+02  -2.2754e+00   3.6718e-02   3.1938e-02   2.4968e+00   5.3182e+00   1.0000e+00

 Run='bcssm-Et.freq.bc3': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          1.76e-07  1.12e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.1163e+03      1  EP     -2.2754e+00   2.5101e+00   7.8922e+02   1.0000e+00   3.6718e-02   3.1938e-02   2.4968e+00   5.3182e+00   1.0000e+00
   10  00:00:00   1.1078e+03      2         -1.9623e+00   2.1987e+00   7.8325e+02   8.5659e-01   3.3826e-02   2.6197e-02   2.5395e+00   5.1730e+00   1.0000e+00
   20  00:00:01   1.1070e+03      3         -1.6966e+00   2.1829e+00   7.8271e+02   8.4853e-01   3.4441e-02   2.4911e-02   2.5175e+00   5.0476e+00   1.0000e+00
   26  00:00:02   1.1076e+03      4  HB     -1.4747e+00   2.2228e+00   7.8317e+02   8.7401e-01   3.5639e-02   2.4564e-02   2.4758e+00   4.9354e+00   1.0000e+00
   30  00:00:02   1.1093e+03      5         -1.2431e+00   2.3046e+00   7.8436e+02   9.3481e-01   3.7497e-02   2.4635e-02   2.4093e+00   4.8028e+00   1.0000e+00
   33  00:00:03   1.1110e+03      6  EP     -1.0983e+00   2.3806e+00   7.8555e+02   1.0000e+00   3.9072e-02   2.4889e-02   2.3537e+00   4.7068e+00   1.0000e+00
Backbone curve along branch point (BP) 35

 Run='bcssm-Et.freq.bp4': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.1114e+03      1  EP      0.0000e+00   2.2950e+00   7.8586e+02   0.0000e+00   1.8892e-02   4.0203e-02   2.8118e+00   5.7611e+00   1.0000e+00
    7  00:00:00   1.1115e+03      2  EP      1.0000e+00   2.2950e+00   7.8586e+02  -2.0121e+00   1.8892e-02   4.0203e-02   2.8118e+00   5.7611e+00   1.0000e+00

 Run='bcssm-Et.freq.bc4': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          4.93e-13  1.11e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.1115e+03      1  EP     -2.0121e+00   2.2950e+00   7.8586e+02   1.0000e+00   1.8892e-02   4.0203e-02   2.8118e+00   5.7611e+00   1.0000e+00
   10  00:00:00   1.0941e+03      2         -2.3759e+00   1.4963e+00   7.7355e+02   6.3474e-01   1.3414e-02   2.5881e-02   3.0294e+00   5.7535e+00   1.0000e+00
   20  00:00:01   1.0884e+03      3         -2.7393e+00   1.1573e+00   7.6936e+02   4.9893e-01   1.1107e-02   1.9682e-02   3.3462e+00   5.7833e+00   1.0000e+00
   30  00:00:02   1.0923e+03      4         -6.2734e+00   1.3512e+00   7.7045e+02   5.3818e-01   1.7310e-02   1.9956e-02   3.4420e+00   5.6652e+00   1.0000e+00
   40  00:00:03   1.0951e+03      5         -7.6471e+00   1.4952e+00   7.7182e+02   5.5860e-01   2.0492e-02   2.0847e-02   3.3780e+00   5.5577e+00   1.0000e+00
   50  00:00:04   1.0956e+03      6         -7.7390e+00   1.5303e+00   7.7218e+02   5.6316e-01   2.1234e-02   2.1075e-02   3.3621e+00   5.5293e+00   1.0000e+00
   53  00:00:04   1.0958e+03      7  FP     -7.7466e+00   1.5442e+00   7.7232e+02   5.6494e-01   2.1522e-02   2.1167e-02   3.3560e+00   5.5181e+00   1.0000e+00
   60  00:00:04   1.0965e+03      8         -7.5095e+00   1.6275e+00   7.7318e+02   5.7582e-01   2.3209e-02   2.1755e-02   3.3212e+00   5.4494e+00   1.0000e+00
   70  00:00:05   1.1002e+03      9         -5.4136e+00   1.9838e+00   7.7702e+02   6.3217e-01   2.9383e-02   2.5224e-02   3.2429e+00   5.2064e+00   1.0000e+00
   80  00:00:06   1.1129e+03     10         -4.1909e+00   2.7283e+00   7.8646e+02   7.9399e-01   3.9753e-02   3.5093e-02   3.2456e+00   5.0138e+00   1.0000e+00
   86  00:00:07   1.1308e+03     11  EP     -3.8325e+00   3.5495e+00   7.9922e+02   1.0000e+00   5.0547e-02   4.6355e-02   3.2606e+00   4.9512e+00   1.0000e+00
Backbone curve along branch point (BP) 41

 Run='bcssm-Et.freq.bp5': Continue until d.obj=1.

 STEP      TIME        ||U||  LABEL  TYPE         d.obj          obj           om        d.eps         rho1         rho2          th1          th2          eps
    0  00:00:00   1.2075e+03      1  EP      0.0000e+00   5.1997e+00   8.5379e+02   0.0000e+00   4.6574e-04   9.8061e-02   3.4218e+00   4.7081e+00   1.0000e+00
    9  00:00:00   1.2078e+03      2  EP      1.0000e+00   5.1997e+00   8.5379e+02  -4.7350e+00   4.6574e-04   9.8061e-02   3.4218e+00   4.7081e+00   1.0000e+00

 Run='bcssm-Et.freq.bc5': Continue along backbone curve.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          3.55e-12  1.21e+03    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE         d.eps          obj           om          eps         rho1         rho2          th1          th2        d.obj
    0  00:00:00   1.2078e+03      1  EP     -4.7350e+00   5.1997e+00   8.5379e+02   1.0000e+00   4.6574e-04   9.8061e-02   3.4218e+00   4.7081e+00   1.0000e+00
   10  00:00:00   1.1561e+03      2         -5.1657e+00   3.6077e+00   8.1718e+02   6.8017e-01   5.2117e-04   6.8875e-02   3.4333e+00   4.7072e+00   1.0000e+00
   20  00:00:01   1.0871e+03      3         -5.3532e+00   3.6127e-01   7.6834e+02   6.7479e-02   3.8890e-04   7.0462e-03   3.5208e+00   4.7130e+00   1.0000e+00
   26  00:00:02   1.0863e+03      4  EP     -5.3541e+00   5.3541e-02   7.6776e+02   1.0000e-02   6.2321e-05   1.0443e-03   3.5230e+00   4.7136e+00   1.0000e+00

timings = 

  struct with fields:

    wa: 31.4584
    wb: 31.3789
    ek: 66.7298

Published with MATLAB® R2023a