Shallow-curved shell structure with geometric nonlinearities

Contents

Finite element model

FEM used in the following reference:

Jain, S., & Tiso, P. (2018). Simulation-free hyper-reduction for geometrically nonlinear structural dynamics: a quadratic manifold lifting approach. Journal of Computational and Nonlinear Dynamics, 13(7), 071003. <https://doi.org/10.1115/1.4040021>

Finite element code taken from the following package:

Jain, S., Marconi, J., Tiso P. (2020). YetAnotherFEcode (Version v1.1). Zenodo. <http://doi.org/10.5281/zenodo.4011282>

System parameters

nDiscretization = 10; % Discretization parameter (#DOFs is proportional to the square of this number)
epsilon = 0.1;        % converge at order 5

Generate model

[M,C,K,fnl,f_0,outdof] = build_model(nDiscretization);
n = length(M); % number of degrees of freedom
disp(['Number of degrees of freedom = ' num2str(n)])
disp(['Phase space dimensionality = ' num2str(2*n)])

Building FE model
Assembling M,C,K matrices
Applying boundary conditions
Solving undamped eigenvalue problem

ans = 

  Patch (Deformed Mesh) with properties:

    FaceColor: 'interp'
    FaceAlpha: 1
    EdgeColor: [0 0 0]
    LineStyle: '-'
        Faces: [400×3 double]
     Vertices: [1200×3 double]

  Use GET to show all properties

Using Rayleigh damping
Assembling external force vector
Getting nonlinearity coefficients
Loaded tensors from storage
Total time spent on model assembly = 00:00:15
Number of degrees of freedom = 1320
Phase space dimensionality = 2640

Dynamical system setup

We consider the forced system

$\mathbf{M}\ddot{\mathbf{x}}+\mathbf{C}\dot{\mathbf{x}}+\mathbf{K}\mathbf{x}+\mathbf{f}(\mathbf{x},\dot{\mathbf{x}})=\epsilon\mathbf{f}^{ext}(\mathbf{\Omega}t),$

which can be written in the first-order form as

$\mathbf{B}\dot{\mathbf{z}}=\mathbf{Az}+\mathbf{F}(\mathbf{z})+\epsilon\mathbf{F}^{ext}(\mathbf{\phi}),\\\dot{\mathbf{\phi}} =\mathbf{\Omega}$

where

$\mathbf{z}=\left[\begin{array}{c}\mathbf{x}\\\dot{\mathbf{x}}\end{array}\right],\quad\mathbf{A}=\left[\begin{array}{cc}-\mathbf{K} &amp; \mathbf{0}\\\mathbf{0} &amp; \mathbf{M}\end{array}\right],\mathbf{B}=\left[\begin{array}{cc}\mathbf{C} &amp; \mathbf{M}\\\mathbf{M} &amp; \mathbf{0}\end{array}\right],\quad\quad\mathbf{F}(\mathbf{z})=\left[\begin{array}{c}\mathbf{-\mathbf{f}(\mathbf{x},\dot{\mathbf{x}})}\\\mathbf{0}\end{array}\right],\quad\mathbf{F}^{ext}(\mathbf{z},\mathbf{\phi})=\left[\begin{array}{c}\mathbf{f}^{ext}(\mathbf{\phi})\\\mathbf{0}\end{array}\right]$.

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

We assume periodic forcing of the form

$\mathbf{f}^{ext}(\phi) = \mathbf{f}_0\cos(\phi)=\frac{\mathbf{f}_0}{2}e^{i\phi} + \frac{\mathbf{f}_0}{2}e^{-i\phi}$

Fourier coefficients of Forcing

kappas = [-1; 1];
coeffs = [f_0 f_0]/2;
DS.add_forcing(coeffs, kappas,epsilon);

Linear Modal analysis and SSM setup

[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 2.000000e-03
modal damping ratio for 2 mode is 2.000000e-03
modal damping ratio for 3 mode is 2.102524e-03
modal damping ratio for 4 mode is 2.141338e-03
modal damping ratio for 5 mode is 2.369557e-03
the left eigenvectors may be incorrect in case of asymmetry of matrices

 The first 10 nonzero eigenvalues are given as 
   1.0e+02 *

  -0.0030 + 1.4922i
  -0.0030 - 1.4922i
  -0.0060 + 2.9878i
  -0.0060 - 2.9878i
  -0.0071 + 3.3973i
  -0.0071 - 3.3973i
  -0.0076 + 3.5356i
  -0.0076 - 3.5356i
  -0.0101 + 4.2617i
  -0.0101 - 4.2617i

Choose Master subspace (perform resonance analysis)

S = SSM(DS);
masterModes = [1,2,3,4];
S.choose_E(masterModes);

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

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

  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i

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

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

  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i

sigma_in = 3

Forced response curves using SSMs

Obtaining forced response curve in reduced-polar coordinate

order = 3;
set(S.Options, 'reltol', 0.5,'IRtol',0.05,'notation', 'multiindex', 'COMPtype', 'first')

choose frequency range around the first natural frequency

set(S.FRCOptions,'coordinates','polar','initialSolver','forward');
set(S.contOptions, 'h_min', 1e-2,'h_max',2,'PtMX',300);
omega0 = imag(S.E.spectrum(1));
omegaRange = omega0*[0.92 1.07];
mFreq = [1 2];

extract forced response curve

p0 = [omegaRange(1) epsilon]';
z0 = 1e-3*[1 1 1 1]';
S.SSM_isol2ep('isol-3',masterModes,order,mFreq,'freq',omegaRange,outdof,{p0,z0});

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

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

  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i

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

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

  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i

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 = 4.41E+00 MB
Manifold computation time at order 3 = 00:00:01
Estimated memory usage at order  3 = 8.92E+00 MB

 Run='isol-3.ep': Continue equilibria along primary branch.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          1.68e+01  1.95e+02    0.0    0.0    0.0
   1   2  2.45e-01  1.84e+00  1.02e+01  1.95e+02    0.0    0.0    0.0
   2   1  8.12e-01  1.25e+00  2.50e+00  1.95e+02    0.0    0.0    0.0
   3   1  1.00e+00  2.80e-01  6.26e-02  1.95e+02    0.0    0.0    0.0
   4   1  1.00e+00  7.64e-03  2.15e-04  1.95e+02    0.0    0.0    0.0
   5   1  1.00e+00  1.59e-06  1.85e-09  1.95e+02    0.0    0.1    0.0
   6   1  1.00e+00  2.69e-12  3.26e-15  1.95e+02    0.0    0.1    0.0

 STEP      TIME        ||U||  LABEL  TYPE            om         rho1         rho2          th1          th2          eps
    0  00:00:00   1.9465e+02      1  EP      1.3729e+02   1.8257e-03   1.9374e-05   9.3997e+00   3.0668e+00   1.0000e-01
   10  00:00:00   1.9817e+02      2          1.3978e+02   2.3109e-03   3.9086e-05   9.3930e+00   3.0470e+00   1.0000e-01
   20  00:00:00   2.0167e+02      3          1.4226e+02   3.1504e-03   9.7874e-05   9.3812e+00   3.0127e+00   1.0000e-01
   30  00:00:00   2.0462e+02      4          1.4435e+02   4.6058e-03   2.9548e-04   9.3597e+00   2.9526e+00   1.0000e-01
   40  00:00:00   2.0679e+02      5          1.4590e+02   7.9885e-03   1.2747e-03   9.2965e+00   2.8013e+00   1.0000e-01
   50  00:00:00   2.0702e+02      6          1.4607e+02   1.0170e-02   2.1632e-03   9.2434e+00   2.6919e+00   1.0000e-01
   52  00:00:01   2.0702e+02      7  SN      1.4607e+02   1.0370e-02   2.2491e-03   9.2381e+00   2.6814e+00   1.0000e-01
   52  00:00:01   2.0702e+02      8  FP      1.4607e+02   1.0370e-02   2.2491e-03   9.2381e+00   2.6814e+00   1.0000e-01
   60  00:00:01   2.0698e+02      9          1.4604e+02   1.1525e-02   2.7508e-03   9.2068e+00   2.6201e+00   1.0000e-01
   70  00:00:01   2.0538e+02     10          1.4493e+02   2.0721e-02   6.6023e-03   8.9307e+00   2.0942e+00   1.0000e-01
   80  00:00:01   2.0056e+02     11          1.4159e+02   3.9002e-02   1.3080e-02   7.9663e+00   2.0028e-01   1.0000e-01
   83  00:00:01   2.0054e+02     12  FP      1.4158e+02   3.9122e-02   1.3141e-02   7.9152e+00   9.8286e-02   1.0000e-01
   83  00:00:01   2.0054e+02     13  SN      1.4158e+02   3.9122e-02   1.3141e-02   7.9152e+00   9.8285e-02   1.0000e-01
   90  00:00:01   2.0075e+02     14          1.4174e+02   3.8710e-02   1.3132e-02   7.7161e+00  -3.0081e-01   1.0000e-01
  100  00:00:01   2.0431e+02     15          1.4429e+02   2.8008e-02   1.0421e-02   7.1018e+00  -1.5512e+00   1.0000e-01
  105  00:00:01   2.1027e+02     16  HB      1.4851e+02   9.2835e-03   6.4952e-03   6.8061e+00  -2.4152e+00   1.0000e-01
  110  00:00:01   2.1091e+02     17          1.4896e+02   7.1734e-03   7.0338e-03   7.0098e+00  -2.2995e+00   1.0000e-01
  120  00:00:01   2.1200e+02     18          1.4966e+02   6.7805e-03   7.7965e-03   8.4475e+00  -1.1611e+00   1.0000e-01
  128  00:00:02   2.1261e+02     19  HB      1.5008e+02   8.9257e-03   7.3949e-03   8.7516e+00  -9.4865e-01   1.0000e-01
  130  00:00:02   2.1281e+02     20          1.5022e+02   9.6293e-03   7.3882e-03   8.7873e+00  -9.3706e-01   1.0000e-01
  140  00:00:02   2.1652e+02     21          1.5286e+02   2.3720e-02   1.1735e-02   8.5045e+00  -1.7629e+00   1.0000e-01
  150  00:00:02   2.1842e+02     22          1.5421e+02   3.1204e-02   1.4754e-02   7.7458e+00  -3.3074e+00   1.0000e-01
  151  00:00:02   2.1842e+02     23  SN      1.5422e+02   3.1152e-02   1.4699e-02   7.7170e+00  -3.3648e+00   1.0000e-01
  151  00:00:02   2.1842e+02     24  FP      1.5422e+02   3.1152e-02   1.4699e-02   7.7170e+00  -3.3648e+00   1.0000e-01
  160  00:00:02   2.1769e+02     25          1.5370e+02   2.6141e-02   1.1526e-02   7.1807e+00  -4.4273e+00   1.0000e-01
  170  00:00:02   2.1568e+02     26          1.5226e+02   1.0990e-02   2.9823e-03   6.5057e+00  -5.7360e+00   1.0000e-01
  172  00:00:02   2.1567e+02     27  FP      1.5226e+02   1.0760e-02   2.8585e-03   6.4981e+00  -5.7510e+00   1.0000e-01
  172  00:00:02   2.1567e+02     28  SN      1.5226e+02   1.0760e-02   2.8585e-03   6.4981e+00  -5.7510e+00   1.0000e-01
  180  00:00:02   2.1573e+02     29          1.5229e+02   9.4942e-03   2.1941e-03   6.4584e+00  -5.8312e+00   1.0000e-01
  190  00:00:02   2.1622e+02     30          1.5264e+02   7.1868e-03   1.1189e-03   6.3975e+00  -5.9635e+00   1.0000e-01
  200  00:00:02   2.1807e+02     31          1.5394e+02   4.7206e-03   3.4419e-04   6.3504e+00  -6.0835e+00   1.0000e-01
  210  00:00:02   2.2044e+02     32          1.5563e+02   3.4197e-03   1.3191e-04   6.3306e+00  -6.1405e+00   1.0000e-01
  220  00:00:02   2.2328e+02     33          1.5763e+02   2.5926e-03   5.7361e-05   6.3189e+00  -6.1756e+00   1.0000e-01
  229  00:00:02   2.2615e+02     34  EP      1.5967e+02   2.0856e-03   2.9775e-05   6.3118e+00  -6.1968e+00   1.0000e-01
the forcing frequency 1.3729e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3736e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3749e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3775e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3808e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3839e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3869e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3897e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3924e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3951e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3978e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4005e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4031e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4057e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4082e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4107e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4131e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4156e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4180e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4203e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4249e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4271e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4293e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4315e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4336e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4357e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4377e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4397e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4416e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4435e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4454e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4472e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4489e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4506e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4522e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4537e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4551e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4565e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4578e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4590e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4600e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4602e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4604e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4605e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4605e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4606e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4606e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4606e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4606e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4606e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4606e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4605e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4604e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4603e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4602e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4600e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4597e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4594e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4588e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4579e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4565e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4541e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4493e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4407e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4306e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4244e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4198e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4179e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4171e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4166e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4163e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4161e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4159e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4159e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4158e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4158e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4158e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4159e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4159e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4160e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4162e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4164e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4166e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4170e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4174e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4179e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4186e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4195e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4205e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4220e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4239e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4265e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4301e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4352e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4429e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4547e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4684e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4753e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4806e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4851e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4853e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4874e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4883e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4888e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4892e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4896e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4899e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4903e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4907e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4911e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4916e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4921e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4927e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4936e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4956e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4966e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4974e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4979e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4984e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4989e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4994e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4999e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5004e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5008e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5009e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5015e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5022e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5030e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5040e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5051e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5065e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5084e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5108e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5140e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5182e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5233e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5286e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5329e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5360e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5381e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5395e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5404e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5411e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5415e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5419e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5421e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5421e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5422e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5422e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5422e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5421e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5419e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5417e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5413e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5408e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5402e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5394e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5383e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5370e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5351e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5326e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5289e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5253e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5237e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5232e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5228e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5227e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5227e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5227e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5228e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5229e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5229e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5230e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5231e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5233e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5234e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5237e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5239e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5243e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5248e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5254e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5264e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5276e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5288e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5299e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5312e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5324e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5338e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5351e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5365e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5379e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5394e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5409e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5425e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5441e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5458e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5474e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5491e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5508e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5526e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5544e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5563e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5581e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5600e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5619e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5639e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5659e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5679e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5699e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5721e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5741e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5763e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5784e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5807e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5829e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5853e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5875e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5899e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5922e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5947e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5967e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02

varargout =

  1×1 cell array

    {1×1 struct}

check the domain of convergence

order = 5;
sol = ep_read_solution('','isol-3.ep',1);
set(S.FRCOptions,'initialSolver','fsolve');
FRC_lead = S.SSM_isol2ep('isol-5',masterModes,order,mFreq,'freq',omegaRange,outdof,{sol.p,sol.x});

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

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

  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i

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

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

  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i

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 = 4.41E+00 MB
Manifold computation time at order 3 = 00:00:01
Estimated memory usage at order  3 = 8.92E+00 MB
Manifold computation time at order 4 = 00:00:04
Estimated memory usage at order  4 = 1.88E+01 MB
Manifold computation time at order 5 = 00:00:10
Estimated memory usage at order  5 = 3.48E+01 MB

Equation solved, inaccuracy possible.

The vector of function values is near zero, as measured by the value
of the function tolerance. However, the last step was ineffective.


 Run='isol-5.ep': Continue equilibria along primary branch.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          1.95e-13  1.94e+02    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE            om         rho1         rho2          th1          th2          eps
    0  00:00:00   1.9425e+02      1  EP      1.3729e+02   1.8257e-03   1.9374e-05   3.1165e+00   3.0668e+00   1.0000e-01
   10  00:00:00   1.9778e+02      2          1.3978e+02   2.3109e-03   3.9085e-05   3.1098e+00   3.0471e+00   1.0000e-01
   20  00:00:00   2.0128e+02      3          1.4226e+02   3.1504e-03   9.7874e-05   3.0980e+00   3.0128e+00   1.0000e-01
   30  00:00:00   2.0424e+02      4          1.4435e+02   4.6060e-03   2.9549e-04   3.0765e+00   2.9527e+00   1.0000e-01
   40  00:00:00   2.0641e+02      5          1.4590e+02   7.9849e-03   1.2733e-03   3.0135e+00   2.8021e+00   1.0000e-01
   50  00:00:00   2.0665e+02      6          1.4607e+02   1.0180e-02   2.1685e-03   2.9601e+00   2.6924e+00   1.0000e-01
   52  00:00:00   2.0665e+02      7  SN      1.4607e+02   1.0379e-02   2.2540e-03   2.9549e+00   2.6821e+00   1.0000e-01
   52  00:00:00   2.0665e+02      8  FP      1.4607e+02   1.0379e-02   2.2540e-03   2.9549e+00   2.6821e+00   1.0000e-01
   60  00:00:00   2.0661e+02      9          1.4604e+02   1.1540e-02   2.7591e-03   2.9236e+00   2.6209e+00   1.0000e-01
   70  00:00:00   2.0506e+02     10          1.4496e+02   2.0617e-02   6.5876e-03   2.6555e+00   2.1123e+00   1.0000e-01
   80  00:00:00   1.9968e+02     11          1.4119e+02   4.1301e-02   1.4043e-02   1.6514e+00   1.4995e-01   1.0000e-01
   82  00:00:00   1.9967e+02     12  SN      1.4118e+02   4.1370e-02   1.4081e-02   1.6184e+00   8.3934e-02   1.0000e-01
   82  00:00:00   1.9967e+02     13  FP      1.4118e+02   4.1370e-02   1.4081e-02   1.6184e+00   8.3933e-02   1.0000e-01
   90  00:00:00   1.9988e+02     14          1.4133e+02   4.0923e-02   1.4043e-02   1.4379e+00  -2.7807e-01   1.0000e-01
  100  00:00:01   2.0375e+02     15          1.4406e+02   2.9135e-02   1.0860e-02   8.3228e-01  -1.5162e+00   1.0000e-01
  106  00:00:01   2.1005e+02     16  HB      1.4851e+02   9.2759e-03   6.5035e-03   5.2382e-01  -2.4143e+00   1.0000e-01
  110  00:00:01   2.1065e+02     17          1.4893e+02   7.2837e-03   6.9854e-03   7.0769e-01  -2.3124e+00   1.0000e-01
  120  00:00:01   2.1156e+02     18          1.4958e+02   6.3941e-03   7.9260e-03   2.0291e+00  -1.2689e+00   1.0000e-01
  128  00:00:01   2.1228e+02     19  HB      1.5008e+02   8.9104e-03   7.3970e-03   2.4663e+00  -9.5064e-01   1.0000e-01
  130  00:00:01   2.1254e+02     20          1.5027e+02   9.8436e-03   7.3998e-03   2.5106e+00  -9.3827e-01   1.0000e-01
  140  00:00:01   2.1641e+02     21          1.5300e+02   2.4442e-02   1.2094e-02   2.1628e+00  -1.8792e+00   1.0000e-01
  150  00:00:01   2.1799e+02     22          1.5410e+02   3.0215e-02   1.4322e-02   1.4306e+00  -3.3630e+00   1.0000e-01
  151  00:00:01   2.1799e+02     23  FP      1.5410e+02   3.0196e-02   1.4303e-02   1.4219e+00  -3.3805e+00   1.0000e-01
  151  00:00:01   2.1799e+02     24  SN      1.5410e+02   3.0196e-02   1.4303e-02   1.4219e+00  -3.3805e+00   1.0000e-01
  160  00:00:01   2.1713e+02     25          1.5346e+02   2.4191e-02   1.0467e-02   8.0331e-01  -4.6064e+00   1.0000e-01
  170  00:00:01   2.1548e+02     26  FP      1.5226e+02   1.0769e-02   2.8653e-03   2.1546e-01  -5.7490e+00   1.0000e-01
  170  00:00:01   2.1548e+02     27  SN      1.5226e+02   1.0769e-02   2.8653e-03   2.1546e-01  -5.7490e+00   1.0000e-01
  170  00:00:01   2.1548e+02     28          1.5226e+02   1.0684e-02   2.8194e-03   2.1266e-01  -5.7546e+00   1.0000e-01
  180  00:00:01   2.1556e+02     29          1.5231e+02   9.2435e-03   2.0675e-03   1.6797e-01  -5.8456e+00   1.0000e-01
  190  00:00:02   2.1632e+02     30          1.5284e+02   6.5603e-03   8.7737e-04   1.0073e-01  -5.9956e+00   1.0000e-01
  200  00:00:02   2.1823e+02     31          1.5419e+02   4.4620e-03   2.9154e-04   6.3079e-02  -6.0949e+00   1.0000e-01
  210  00:00:02   2.2069e+02     32          1.5593e+02   3.2596e-03   1.1423e-04   4.5139e-02  -6.1473e+00   1.0000e-01
  220  00:00:02   2.2360e+02     33          1.5799e+02   2.4864e-03   5.0568e-05   3.4219e-02  -6.1800e+00   1.0000e-01
  228  00:00:02   2.2598e+02     34  EP      1.5967e+02   2.0856e-03   2.9774e-05   2.8651e-02  -6.1968e+00   1.0000e-01
the forcing frequency 1.3729e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3736e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3749e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3775e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3808e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3839e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3869e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3897e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3924e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3951e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.3978e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4005e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4031e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4057e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4082e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4107e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4131e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4156e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4180e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4203e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4249e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4271e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4293e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4315e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4336e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4357e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4377e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4397e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4416e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4435e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4454e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4472e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4489e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4506e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4522e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4537e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4551e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4565e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4578e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4590e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4600e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4602e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4604e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4605e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4605e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4606e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4606e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4607e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4606e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4606e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4606e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4605e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4604e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4603e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4602e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4600e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4597e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4594e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4588e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4580e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4566e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4542e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4496e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4408e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4292e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4168e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4143e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4132e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4127e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4123e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4121e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4119e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4119e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4118e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4118e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4118e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4118e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4118e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4119e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4120e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4122e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4124e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4126e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4129e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4133e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4138e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4145e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4153e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4164e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4178e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4197e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4223e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4261e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4318e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4406e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4542e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4679e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4749e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4806e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4850e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4851e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4871e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4880e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4885e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4889e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4893e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4897e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4901e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4905e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4909e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4913e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4917e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4923e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4930e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4943e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4958e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4972e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4982e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4987e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4992e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.4997e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5002e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5007e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5008e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5013e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5019e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5027e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5035e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5046e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5059e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5075e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5096e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5124e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5161e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5206e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5255e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5300e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5334e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5358e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5375e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5387e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5395e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5401e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5405e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5408e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5409e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5410e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5410e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5410e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5410e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5409e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5406e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5403e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5399e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5393e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5385e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5375e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5363e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5346e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5324e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5292e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5260e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5235e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5229e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5227e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5226e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5227e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5227e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5228e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5228e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5229e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5230e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5231e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5232e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5234e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5236e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5238e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5242e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5246e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5252e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5261e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5274e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5284e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5296e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5307e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5320e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5333e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5347e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5360e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5375e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5389e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5405e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5419e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5436e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5452e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5469e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5485e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5503e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5520e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5538e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5556e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5575e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5593e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5613e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5632e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5652e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5672e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5693e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5713e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5735e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5756e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5778e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5799e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5822e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5844e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5868e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5890e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5915e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5938e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5963e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02
the forcing frequency 1.5967e+02 is nearly resonant with the eigenvalue -2.9845e-01 + i1.4922e+02

varargout =

  1×1 cell array

    {1×1 struct}

check the effects of non-autonomous part

set(S.Options, 'contribNonAuto',false);
FRC_zero = S.SSM_isol2ep('isol-5',masterModes,order,mFreq,'freq',omegaRange,outdof,{sol.p,sol.x});

% 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(:,2),FRC.st,ST,legs,legu);
    SNfig = plot(FRC.om(SNidx),FRC.Aout_frc(SNidx,2),thm.SN{:});
    set(get(get(SNfig,'Annotation'),'LegendInformation'),...
    'IconDisplayStyle','off');
    HBfig = plot(FRC.om(HBidx),FRC.Aout_frc(HBidx,2),thm.HB{:});
    set(get(get(HBfig,'Annotation'),'LegendInformation'),...
    'IconDisplayStyle','off');
    xlabel('$\Omega$','Interpreter','latex');
    ylabel('$||w_B||_{\infty}$','Interpreter','latex');
    set(gca,'FontSize',14);
    grid on; axis tight;
end
legend boxoff

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

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

  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i

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

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

  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i

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 = 4.41E+00 MB
Manifold computation time at order 3 = 00:00:01
Estimated memory usage at order  3 = 8.92E+00 MB
Manifold computation time at order 4 = 00:00:04
Estimated memory usage at order  4 = 1.88E+01 MB
Manifold computation time at order 5 = 00:00:09
Estimated memory usage at order  5 = 3.48E+01 MB

Equation solved, inaccuracy possible.

The vector of function values is near zero, as measured by the value
of the function tolerance. However, the last step was ineffective.


 Run='isol-5.ep': Continue equilibria along primary branch.

    STEP   DAMPING               NORMS              COMPUTATION TIMES
  IT SIT     GAMMA     ||d||     ||f||     ||U||   F(x)  DF(x)  SOLVE
   0                          1.95e-13  1.94e+02    0.0    0.0    0.0

 STEP      TIME        ||U||  LABEL  TYPE            om         rho1         rho2          th1          th2          eps
    0  00:00:00   1.9425e+02      1  EP      1.3729e+02   1.8257e-03   1.9374e-05   3.1165e+00   3.0668e+00   1.0000e-01
   10  00:00:00   1.9778e+02      2          1.3978e+02   2.3109e-03   3.9085e-05   3.1098e+00   3.0471e+00   1.0000e-01
   20  00:00:00   2.0128e+02      3          1.4226e+02   3.1504e-03   9.7874e-05   3.0980e+00   3.0128e+00   1.0000e-01
   30  00:00:00   2.0424e+02      4          1.4435e+02   4.6060e-03   2.9549e-04   3.0765e+00   2.9527e+00   1.0000e-01
   40  00:00:00   2.0641e+02      5          1.4590e+02   7.9849e-03   1.2733e-03   3.0135e+00   2.8021e+00   1.0000e-01
   50  00:00:00   2.0665e+02      6          1.4607e+02   1.0180e-02   2.1685e-03   2.9601e+00   2.6924e+00   1.0000e-01
   52  00:00:00   2.0665e+02      7  SN      1.4607e+02   1.0379e-02   2.2540e-03   2.9549e+00   2.6821e+00   1.0000e-01
   52  00:00:00   2.0665e+02      8  FP      1.4607e+02   1.0379e-02   2.2540e-03   2.9549e+00   2.6821e+00   1.0000e-01
   60  00:00:00   2.0661e+02      9          1.4604e+02   1.1540e-02   2.7591e-03   2.9236e+00   2.6209e+00   1.0000e-01
   70  00:00:00   2.0506e+02     10          1.4496e+02   2.0617e-02   6.5876e-03   2.6555e+00   2.1123e+00   1.0000e-01
   80  00:00:00   1.9968e+02     11          1.4119e+02   4.1301e-02   1.4043e-02   1.6514e+00   1.4995e-01   1.0000e-01
   82  00:00:00   1.9967e+02     12  SN      1.4118e+02   4.1370e-02   1.4081e-02   1.6184e+00   8.3934e-02   1.0000e-01
   82  00:00:00   1.9967e+02     13  FP      1.4118e+02   4.1370e-02   1.4081e-02   1.6184e+00   8.3933e-02   1.0000e-01
   90  00:00:00   1.9988e+02     14          1.4133e+02   4.0923e-02   1.4043e-02   1.4379e+00  -2.7807e-01   1.0000e-01
  100  00:00:00   2.0375e+02     15          1.4406e+02   2.9135e-02   1.0860e-02   8.3228e-01  -1.5162e+00   1.0000e-01
  106  00:00:00   2.1005e+02     16  HB      1.4851e+02   9.2759e-03   6.5035e-03   5.2382e-01  -2.4143e+00   1.0000e-01
  110  00:00:01   2.1065e+02     17          1.4893e+02   7.2837e-03   6.9854e-03   7.0769e-01  -2.3124e+00   1.0000e-01
  120  00:00:01   2.1156e+02     18          1.4958e+02   6.3941e-03   7.9260e-03   2.0291e+00  -1.2689e+00   1.0000e-01
  128  00:00:01   2.1228e+02     19  HB      1.5008e+02   8.9104e-03   7.3970e-03   2.4663e+00  -9.5064e-01   1.0000e-01
  130  00:00:01   2.1254e+02     20          1.5027e+02   9.8436e-03   7.3998e-03   2.5106e+00  -9.3827e-01   1.0000e-01
  140  00:00:01   2.1641e+02     21          1.5300e+02   2.4442e-02   1.2094e-02   2.1628e+00  -1.8792e+00   1.0000e-01
  150  00:00:01   2.1799e+02     22          1.5410e+02   3.0215e-02   1.4322e-02   1.4306e+00  -3.3630e+00   1.0000e-01
  151  00:00:01   2.1799e+02     23  FP      1.5410e+02   3.0196e-02   1.4303e-02   1.4219e+00  -3.3805e+00   1.0000e-01
  151  00:00:01   2.1799e+02     24  SN      1.5410e+02   3.0196e-02   1.4303e-02   1.4219e+00  -3.3805e+00   1.0000e-01
  160  00:00:01   2.1713e+02     25          1.5346e+02   2.4191e-02   1.0467e-02   8.0331e-01  -4.6064e+00   1.0000e-01
  170  00:00:01   2.1548e+02     26  FP      1.5226e+02   1.0769e-02   2.8653e-03   2.1546e-01  -5.7490e+00   1.0000e-01
  170  00:00:01   2.1548e+02     27  SN      1.5226e+02   1.0769e-02   2.8653e-03   2.1546e-01  -5.7490e+00   1.0000e-01
  170  00:00:01   2.1548e+02     28          1.5226e+02   1.0684e-02   2.8194e-03   2.1266e-01  -5.7546e+00   1.0000e-01
  180  00:00:01   2.1556e+02     29          1.5231e+02   9.2435e-03   2.0675e-03   1.6797e-01  -5.8456e+00   1.0000e-01
  190  00:00:01   2.1632e+02     30          1.5284e+02   6.5603e-03   8.7737e-04   1.0073e-01  -5.9956e+00   1.0000e-01
  200  00:00:01   2.1823e+02     31          1.5419e+02   4.4620e-03   2.9154e-04   6.3079e-02  -6.0949e+00   1.0000e-01
  210  00:00:01   2.2069e+02     32          1.5593e+02   3.2596e-03   1.1423e-04   4.5139e-02  -6.1473e+00   1.0000e-01
  220  00:00:01   2.2360e+02     33          1.5799e+02   2.4864e-03   5.0568e-05   3.4219e-02  -6.1800e+00   1.0000e-01
  228  00:00:02   2.2598e+02     34  EP      1.5967e+02   2.0856e-03   2.9774e-05   2.8651e-02  -6.1968e+00   1.0000e-01

varargout =

  1×1 cell array

    {1×1 struct}

Extract ridges and trenches of FRS in $\mathcal{L}_2$ norm

startdof1 = tic;
optdof = outdof(1);
set(S.contOptions, 'h0',1e-1,'h_min',1e-3,'h_max',5, 'PtMX', 250, 'MaxRes', 0.1);  % continuation setting
epsRange = [0.01 1]*epsilon;
parRange = {omegaRange,epsRange};
sol = ep_read_solution('','isol-5.ep',1);
set(S.FRSOptions, 'calFRS', true);
set(S.FRCOptions,'coordinates','polar','initialSolver','fsolve');
set(S.FRCOptions,'DBCobjnorm','l2','DBCstepFactor', [10 100]);
S.extract_ridges_trenches('bcssm-dof1',masterModes,order,mFreq,parRange,outdof,optdof,{sol.p,sol.x});
timings.dof1 = toc(startdof1)

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

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

  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i

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

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

  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i

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 = 4.41E+00 MB
Manifold computation time at order 3 = 00:00:01
Estimated memory usage at order  3 = 8.92E+00 MB
Manifold computation time at order 4 = 00:00:04
Estimated memory usage at order  4 = 1.88E+01 MB
Manifold computation time at order 5 = 00:00:10
Estimated memory usage at order  5 = 3.48E+01 MB

Equation solved, solver stalled.

fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared and the vector of function values
is near zero as measured by the value of the function tolerance.


 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                          7.08e-16  1.94e+02    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   1.9425e+02      1  EP      6.7851e-05   0.0000e+00   1.3729e+02   0.0000e+00   1.8257e-03   1.9374e-05   3.1165e+00   3.0668e+00   1.0000e-01
   10  00:00:00   1.9778e+02      2          8.5885e-05   0.0000e+00   1.3978e+02   0.0000e+00   2.3109e-03   3.9085e-05   3.1098e+00   3.0471e+00   1.0000e-01
   20  00:00:00   2.0128e+02      3          1.1710e-04   0.0000e+00   1.4226e+02   0.0000e+00   3.1504e-03   9.7875e-05   3.0980e+00   3.0128e+00   1.0000e-01
   30  00:00:01   2.0424e+02      4          1.7126e-04   0.0000e+00   1.4435e+02   0.0000e+00   4.6060e-03   2.9549e-04   3.0765e+00   2.9527e+00   1.0000e-01
   40  00:00:01   2.0641e+02      5          2.9739e-04   0.0000e+00   1.4590e+02   0.0000e+00   7.9849e-03   1.2733e-03   3.0135e+00   2.8021e+00   1.0000e-01
   50  00:00:01   2.0665e+02      6          3.7859e-04   0.0000e+00   1.4607e+02   0.0000e+00   1.0150e-02   2.1554e-03   2.9609e+00   2.6940e+00   1.0000e-01
   53  00:00:02   2.0665e+02      7  SN      3.8722e-04   0.0000e+00   1.4607e+02   0.0000e+00   1.0379e-02   2.2540e-03   2.9549e+00   2.6821e+00   1.0000e-01
   60  00:00:02   2.0662e+02      8          4.2435e-04   0.0000e+00   1.4605e+02   0.0000e+00   1.1366e-02   2.6830e-03   2.9284e+00   2.6302e+00   1.0000e-01
   70  00:00:02   2.0568e+02      9          6.6617e-04   0.0000e+00   1.4539e+02   0.0000e+00   1.7753e-02   5.4286e-03   2.7424e+00   2.2770e+00   1.0000e-01
   80  00:00:03   1.9971e+02     10          1.5765e-03   0.0000e+00   1.4120e+02   0.0000e+00   4.1159e-02   1.3980e-02   1.6907e+00   2.2833e-01   1.0000e-01
   84  00:00:03   1.9967e+02     11  SN      1.5850e-03   0.0000e+00   1.4118e+02   0.0000e+00   4.1370e-02   1.4081e-02   1.6184e+00   8.3934e-02   1.0000e-01
   85  00:00:03   1.9968e+02     12  BP      1.5859e-03   0.0000e+00   1.4119e+02   0.0000e+00   4.1393e-02   1.4105e-02   1.5851e+00   1.7330e-02   1.0000e-01
   85  00:00:03   1.9968e+02     13  FP      1.5859e-03   0.0000e+00   1.4119e+02   0.0000e+00   4.1393e-02   1.4105e-02   1.5851e+00   1.7329e-02   1.0000e-01
   90  00:00:03   1.9980e+02     14          1.5765e-03   0.0000e+00   1.4127e+02   0.0000e+00   4.1154e-02   1.4089e-02   1.4803e+00  -1.9265e-01   1.0000e-01
  100  00:00:03   2.0189e+02     15          1.3318e-03   0.0000e+00   1.4275e+02   0.0000e+00   3.4945e-02   1.2483e-02   1.0400e+00  -1.0860e+00   1.0000e-01
  107  00:00:04   2.1005e+02     16  HB      3.4827e-04   0.0000e+00   1.4851e+02   0.0000e+00   9.2759e-03   6.5035e-03   5.2382e-01  -2.4143e+00   1.0000e-01
  110  00:00:04   2.1046e+02     17          2.9726e-04   0.0000e+00   1.4880e+02   0.0000e+00   7.9146e-03   6.7577e-03   6.2084e-01  -2.3691e+00   1.0000e-01
  120  00:00:04   2.1107e+02     18          2.2555e-04   0.0000e+00   1.4923e+02   0.0000e+00   6.0120e-03   7.7951e-03   1.1564e+00  -1.9716e+00   1.0000e-01
  122  00:00:04   2.1125e+02     19  BP      2.1799e-04   0.0000e+00   1.4936e+02   0.0000e+00   5.8305e-03   8.0546e-03   1.4994e+00  -1.6973e+00   1.0000e-01
  122  00:00:04   2.1125e+02     20  FP      2.1799e-04   0.0000e+00   1.4936e+02   0.0000e+00   5.8305e-03   8.0548e-03   1.4999e+00  -1.6969e+00   1.0000e-01
  130  00:00:05   2.1226e+02     21          3.2632e-04   0.0000e+00   1.5007e+02   0.0000e+00   8.8375e-03   7.4006e-03   2.4615e+00  -9.5284e-01   1.0000e-01
  131  00:00:05   2.1228e+02     22  HB      3.2899e-04   0.0000e+00   1.5008e+02   0.0000e+00   8.9104e-03   7.3970e-03   2.4663e+00  -9.5064e-01   1.0000e-01
  140  00:00:05   2.1443e+02     23          6.1401e-04   0.0000e+00   1.5160e+02   0.0000e+00   1.6672e-02   9.0066e-03   2.4650e+00  -1.2218e+00   1.0000e-01
  150  00:00:05   2.1791e+02     24          1.1094e-03   0.0000e+00   1.5405e+02   0.0000e+00   3.0204e-02   1.4473e-02   1.5902e+00  -3.0433e+00   1.0000e-01
  152  00:00:06   2.1797e+02     25  BP      1.1127e-03   0.0000e+00   1.5409e+02   0.0000e+00   3.0291e-02   1.4438e-02   1.5066e+00  -3.2111e+00   1.0000e-01
  152  00:00:06   2.1797e+02     26  FP      1.1127e-03   0.0000e+00   1.5409e+02   0.0000e+00   3.0291e-02   1.4438e-02   1.5066e+00  -3.2111e+00   1.0000e-01
  154  00:00:06   2.1799e+02     27  SN      1.1094e-03   0.0000e+00   1.5410e+02   0.0000e+00   3.0196e-02   1.4303e-02   1.4219e+00  -3.3805e+00   1.0000e-01
  160  00:00:06   2.1767e+02     28          1.0148e-03   0.0000e+00   1.5385e+02   0.0000e+00   2.7588e-02   1.2520e-02   1.0430e+00  -4.1341e+00   1.0000e-01
  170  00:00:06   2.1548e+02     29          4.2273e-04   0.0000e+00   1.5226e+02   0.0000e+00   1.1410e-02   3.2127e-03   2.3697e-01  -5.7063e+00   1.0000e-01
  173  00:00:07   2.1548e+02     30  SN      3.9911e-04   0.0000e+00   1.5226e+02   0.0000e+00   1.0769e-02   2.8653e-03   2.1546e-01  -5.7490e+00   1.0000e-01
  180  00:00:07   2.1551e+02     31          3.6020e-04   0.0000e+00   1.5228e+02   0.0000e+00   9.7142e-03   2.3079e-03   1.8201e-01  -5.8166e+00   1.0000e-01
  190  00:00:07   2.1584e+02     32          2.8842e-04   0.0000e+00   1.5250e+02   0.0000e+00   7.7712e-03   1.3671e-03   1.2822e-01  -5.9313e+00   1.0000e-01
  200  00:00:07   2.1752e+02     33          1.8672e-04   0.0000e+00   1.5369e+02   0.0000e+00   5.0263e-03   4.1343e-04   7.2203e-02  -6.0694e+00   1.0000e-01
  210  00:00:08   2.1980e+02     34          1.3411e-04   0.0000e+00   1.5530e+02   0.0000e+00   3.6092e-03   1.5505e-04   5.0200e-02  -6.1323e+00   1.0000e-01
  220  00:00:08   2.2256e+02     35          1.0095e-04   0.0000e+00   1.5725e+02   0.0000e+00   2.7166e-03   6.6019e-05   3.7439e-02  -6.1703e+00   1.0000e-01
  230  00:00:08   2.2576e+02     36          7.8661e-05   0.0000e+00   1.5952e+02   0.0000e+00   2.1167e-03   3.1134e-05   2.9082e-02  -6.1955e+00   1.0000e-01
  231  00:00:08   2.2598e+02     37  EP      7.7504e-05   0.0000e+00   1.5967e+02   0.0000e+00   2.0856e-03   2.9774e-05   2.8651e-02  -6.1968e+00   1.0000e-01
Backbone curve along branch point (BP) 12

 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   1.9968e+02      1  EP      0.0000e+00   1.5859e-03   1.4119e+02   0.0000e+00   4.1393e-02   1.4105e-02   1.5851e+00   1.7330e-02   1.0000e-01
    1  00:00:00   1.9968e+02      2  BP      6.1300e-08   1.5859e-03   1.4119e+02  -1.0395e-09   4.1393e-02   1.4105e-02   1.5851e+00   1.7330e-02   1.0000e-01
    5  00:00:00   1.9968e+02      3  EP      1.0000e+00   1.5859e-03   1.4119e+02  -1.6957e-02   4.1393e-02   1.4105e-02   1.5851e+00   1.7330e-02   1.0000e-01

 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                          2.18e-11  2.00e+02    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   1.9968e+02      1  EP     -1.6957e-02   1.5859e-03   1.4119e+02   1.0000e-01   4.1393e-02   1.4105e-02   1.5851e+00   1.7330e-02   1.0000e+00
    3  00:00:00   2.0005e+02      2  FP     -1.6962e-02   1.5379e-03   1.4145e+02   9.7170e-02   4.0184e-02   1.3743e-02   1.5866e+00   1.8238e-02   1.0000e+00
   10  00:00:00   2.1006e+02      3  FP     -1.4011e-02   1.5736e-04   1.4853e+02   9.7719e-03   4.2253e-03   1.3672e-03   1.8227e+00   1.7422e-01   1.0000e+00
   10  00:00:00   2.1017e+02      4         -1.4026e-02   1.4149e-04   1.4860e+02   8.6400e-03   3.8003e-03   1.1975e-03   1.8349e+00   1.6978e-01   1.0000e+00
   20  00:00:00   2.1069e+02      5         -1.5411e-02   6.4426e-05   1.4897e+02   3.2895e-03   1.7326e-03   4.0695e-04   1.8448e+00  -6.4660e-02   1.0000e+00
   27  00:00:01   2.1098e+02      6  EP     -2.1224e-02   2.4639e-05   1.4917e+02   1.0000e-03   6.6296e-04   8.3499e-05   1.6645e+00  -7.5065e-01   1.0000e+00
Backbone curve along branch point (BP) 19

 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   2.1125e+02      1  EP      0.0000e+00   2.1799e-04   1.4936e+02   0.0000e+00   5.8305e-03   8.0546e-03   1.4994e+00  -1.6973e+00   1.0000e-01
    5  00:00:00   2.1125e+02      2  EP      1.0000e+00   2.1801e-04   1.4936e+02  -7.7473e-04   5.8311e-03   8.0545e-03   1.4994e+00  -1.6973e+00   1.0000e-01

 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                          2.88e-14  2.11e+02    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   2.1125e+02      1  EP     -7.7473e-04   2.1801e-04   1.4936e+02   1.0000e-01   5.8311e-03   8.0545e-03   1.4994e+00  -1.6973e+00   1.0000e+00
   10  00:00:00   2.1128e+02      2  HB     -2.6801e-03   1.1211e-04   1.4937e+02   1.6928e-02   3.0115e-03   2.1371e-03   1.3952e+00  -1.8674e+00   1.0000e+00
   10  00:00:00   2.1128e+02      3         -3.3169e-03   9.9354e-05   1.4938e+02   1.2636e-02   2.6700e-03   1.6793e-03   1.3757e+00  -1.9077e+00   1.0000e+00
   18  00:00:00   2.1166e+02      4  FP     -1.1751e-02   5.9506e-05   1.4962e+02   3.9454e-03   1.6015e-03   4.7859e-04   1.0285e+00  -3.3126e+00   1.0000e+00
   20  00:00:00   2.1178e+02      5  FP     -1.1738e-02   7.3508e-05   1.4971e+02   5.1377e-03   1.9786e-03   6.3554e-04   1.0292e+00  -3.4652e+00   1.0000e+00
   20  00:00:00   2.1179e+02      6         -1.1738e-02   7.4848e-05   1.4971e+02   5.2519e-03   2.0147e-03   6.5111e-04   1.0306e+00  -3.4737e+00   1.0000e+00
   30  00:00:01   2.1202e+02      7         -1.1848e-02   1.0848e-04   1.4987e+02   8.1065e-03   2.9212e-03   1.0587e-03   1.0887e+00  -3.5522e+00   1.0000e+00
   37  00:00:01   2.1275e+02      8  FP     -1.2179e-02   2.2598e-04   1.5039e+02   1.7842e-02   6.0958e-03   2.5302e-03   1.2736e+00  -3.4449e+00   1.0000e+00
   40  00:00:01   2.1397e+02      9         -1.1756e-02   4.2606e-04   1.5126e+02   3.4493e-02   1.1523e-02   5.0259e-03   1.4021e+00  -3.3214e+00   1.0000e+00
   44  00:00:01   2.1797e+02     10  EP     -9.3231e-03   1.1127e-03   1.5409e+02   1.0000e-01   3.0291e-02   1.4438e-02   1.5066e+00  -3.2111e+00   1.0000e+00
Backbone curve along branch point (BP) 25

 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   2.1797e+02      1  EP      0.0000e+00   1.1127e-03   1.5409e+02   0.0000e+00   3.0291e-02   1.4438e-02   1.5066e+00  -3.2111e+00   1.0000e-01
    5  00:00:00   2.1798e+02      2  EP      1.0000e+00   1.1127e-03   1.5409e+02  -9.3231e-03   3.0291e-02   1.4438e-02   1.5066e+00  -3.2111e+00   1.0000e-01

 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                          1.30e-07  2.18e+02    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   2.1797e+02      1  EP     -9.3231e-03   1.1127e-03   1.5409e+02   1.0000e-01   3.0291e-02   1.4438e-02   1.5066e+00  -3.2111e+00   1.0000e+00
    8  00:00:00   2.1275e+02      2  FP     -1.2179e-02   2.2613e-04   1.5039e+02   1.7854e-02   6.0999e-03   2.5321e-03   1.2737e+00  -3.4448e+00   1.0000e+00
   10  00:00:00   2.1194e+02      3         -1.1790e-02   9.5883e-05   1.4982e+02   7.0410e-03   2.5816e-03   9.0329e-04   1.0641e+00  -3.5429e+00   1.0000e+00
   18  00:00:00   2.1178e+02      4  FP     -1.1738e-02   7.3510e-05   1.4971e+02   5.1379e-03   1.9787e-03   6.3556e-04   1.0292e+00  -3.4652e+00   1.0000e+00
   20  00:00:00   2.1173e+02      5         -1.1742e-02   6.7277e-05   1.4967e+02   4.6069e-03   1.8107e-03   5.6425e-04   1.0251e+00  -3.4145e+00   1.0000e+00
   23  00:00:00   2.1166e+02      6  FP     -1.1751e-02   5.9521e-05   1.4962e+02   3.9467e-03   1.6018e-03   4.7875e-04   1.0284e+00  -3.3128e+00   1.0000e+00
   30  00:00:01   2.1128e+02      7         -3.3675e-03   9.8492e-05   1.4938e+02   1.2378e-02   2.6469e-03   1.6504e-03   1.3743e+00  -1.9108e+00   1.0000e+00
   31  00:00:01   2.1128e+02      8  HB     -2.6844e-03   1.1201e-04   1.4937e+02   1.6891e-02   3.0088e-03   2.1333e-03   1.3950e+00  -1.8677e+00   1.0000e+00
   38  00:00:01   2.1125e+02      9  EP     -7.7473e-04   2.1801e-04   1.4936e+02   1.0000e-01   5.8311e-03   8.0545e-03   1.4994e+00  -1.6973e+00   1.0000e+00

timings = 

  struct with fields:

    dof1: 34.2119

Change optdof and see what happens

startdof2 = tic;
optdof = outdof(2);
S.extract_ridges_trenches('bcssm-dof2',masterModes,order,mFreq,parRange,outdof,optdof,{sol.p,sol.x});
timings.dof2 = toc(startdof2)

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

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

  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 + 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0071 - 3.3973i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 + 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0076 - 3.5356i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 + 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i
  -0.0101 - 4.2617i

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

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

  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 + 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0030 - 1.4922i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 + 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i
  -0.0060 - 2.9878i

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 = 4.41E+00 MB
Manifold computation time at order 3 = 00:00:01
Estimated memory usage at order  3 = 8.92E+00 MB
Manifold computation time at order 4 = 00:00:03
Estimated memory usage at order  4 = 1.88E+01 MB
Manifold computation time at order 5 = 00:00:09
Estimated memory usage at order  5 = 3.48E+01 MB

Equation solved, solver stalled.

fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared and the vector of function values
is near zero as measured by the value of the function tolerance.


 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                          7.08e-16  1.94e+02    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   1.9425e+02      1  EP      1.1145e-06   0.0000e+00   1.3729e+02   0.0000e+00   1.8257e-03   1.9374e-05   3.1165e+00   3.0668e+00   1.0000e-01
   10  00:00:00   1.9778e+02      2          2.1403e-06   0.0000e+00   1.3978e+02   0.0000e+00   2.3109e-03   3.9085e-05   3.1098e+00   3.0471e+00   1.0000e-01
   20  00:00:00   2.0128e+02      3          5.0966e-06   0.0000e+00   1.4226e+02   0.0000e+00   3.1504e-03   9.7875e-05   3.0980e+00   3.0128e+00   1.0000e-01
   30  00:00:00   2.0424e+02      4          1.4736e-05   0.0000e+00   1.4435e+02   0.0000e+00   4.6060e-03   2.9549e-04   3.0765e+00   2.9527e+00   1.0000e-01
   40  00:00:01   2.0641e+02      5          6.1493e-05   0.0000e+00   1.4590e+02   0.0000e+00   7.9849e-03   1.2733e-03   3.0135e+00   2.8021e+00   1.0000e-01
   50  00:00:01   2.0665e+02      6          1.0375e-04   0.0000e+00   1.4607e+02   0.0000e+00   1.0150e-02   2.1554e-03   2.9609e+00   2.6940e+00   1.0000e-01
   53  00:00:01   2.0665e+02      7  SN      1.0850e-04   0.0000e+00   1.4607e+02   0.0000e+00   1.0379e-02   2.2540e-03   2.9549e+00   2.6821e+00   1.0000e-01
   60  00:00:01   2.0662e+02      8          1.2922e-04   0.0000e+00   1.4605e+02   0.0000e+00   1.1366e-02   2.6830e-03   2.9284e+00   2.6302e+00   1.0000e-01
   70  00:00:02   2.0568e+02      9          2.6555e-04   0.0000e+00   1.4539e+02   0.0000e+00   1.7753e-02   5.4286e-03   2.7424e+00   2.2770e+00   1.0000e-01
   80  00:00:02   1.9971e+02     10          7.5403e-04   0.0000e+00   1.4120e+02   0.0000e+00   4.1159e-02   1.3980e-02   1.6907e+00   2.2833e-01   1.0000e-01
   84  00:00:02   1.9967e+02     11  SN      7.5994e-04   0.0000e+00   1.4118e+02   0.0000e+00   4.1370e-02   1.4081e-02   1.6184e+00   8.3934e-02   1.0000e-01
   87  00:00:02   1.9970e+02     12  BP      7.6149e-04   0.0000e+00   1.4120e+02   0.0000e+00   4.1376e-02   1.4114e-02   1.5579e+00  -3.6984e-02   1.0000e-01
   90  00:00:03   1.9980e+02     13          7.5892e-04   0.0000e+00   1.4127e+02   0.0000e+00   4.1154e-02   1.4089e-02   1.4803e+00  -1.9265e-01   1.0000e-01
  100  00:00:03   2.0189e+02     14          6.4993e-04   0.0000e+00   1.4275e+02   0.0000e+00   3.4945e-02   1.2483e-02   1.0400e+00  -1.0860e+00   1.0000e-01
  107  00:00:03   2.0987e+02     15  FP      2.9640e-04   0.0000e+00   1.4838e+02   0.0000e+00   9.8511e-03   6.4680e-03   5.0311e-01  -2.4159e+00   1.0000e-01
  107  00:00:03   2.0987e+02     16  BP      2.9640e-04   0.0000e+00   1.4838e+02   0.0000e+00   9.8510e-03   6.4680e-03   5.0311e-01  -2.4159e+00   1.0000e-01
  107  00:00:03   2.1005e+02     17  HB      2.9718e-04   0.0000e+00   1.4851e+02   0.0000e+00   9.2759e-03   6.5035e-03   5.2382e-01  -2.4143e+00   1.0000e-01
  110  00:00:03   2.1046e+02     18          3.0681e-04   0.0000e+00   1.4880e+02   0.0000e+00   7.9146e-03   6.7577e-03   6.2084e-01  -2.3691e+00   1.0000e-01
  120  00:00:04   2.1107e+02     19          3.5061e-04   0.0000e+00   1.4923e+02   0.0000e+00   6.0120e-03   7.7951e-03   1.1564e+00  -1.9716e+00   1.0000e-01
  122  00:00:04   2.1132e+02     20  FP      3.6216e-04   0.0000e+00   1.4941e+02   0.0000e+00   5.8687e-03   8.0821e-03   1.6302e+00  -1.5916e+00   1.0000e-01
  122  00:00:04   2.1132e+02     21  BP      3.6216e-04   0.0000e+00   1.4941e+02   0.0000e+00   5.8688e-03   8.0821e-03   1.6304e+00  -1.5915e+00   1.0000e-01
  130  00:00:04   2.1226e+02     22          3.2705e-04   0.0000e+00   1.5007e+02   0.0000e+00   8.8375e-03   7.4006e-03   2.4615e+00  -9.5284e-01   1.0000e-01
  131  00:00:04   2.1228e+02     23  HB      3.2679e-04   0.0000e+00   1.5008e+02   0.0000e+00   8.9104e-03   7.3970e-03   2.4663e+00  -9.5064e-01   1.0000e-01
  133  00:00:05   2.1249e+02     24  BP      3.2559e-04   0.0000e+00   1.5023e+02   0.0000e+00   9.6445e-03   7.3919e-03   2.5034e+00  -9.3877e-01   1.0000e-01
  140  00:00:05   2.1443e+02     25          3.8589e-04   0.0000e+00   1.5160e+02   0.0000e+00   1.6672e-02   9.0066e-03   2.4650e+00  -1.2218e+00   1.0000e-01
  150  00:00:05   2.1791e+02     26  BP      5.9235e-04   0.0000e+00   1.5405e+02   0.0000e+00   3.0203e-02   1.4473e-02   1.5907e+00  -3.0424e+00   1.0000e-01
  150  00:00:05   2.1791e+02     27          5.9235e-04   0.0000e+00   1.5405e+02   0.0000e+00   3.0204e-02   1.4473e-02   1.5902e+00  -3.0433e+00   1.0000e-01
  154  00:00:05   2.1799e+02     28  SN      5.8474e-04   0.0000e+00   1.5410e+02   0.0000e+00   3.0196e-02   1.4303e-02   1.4219e+00  -3.3805e+00   1.0000e-01
  160  00:00:06   2.1767e+02     29          5.1360e-04   0.0000e+00   1.5385e+02   0.0000e+00   2.7588e-02   1.2520e-02   1.0430e+00  -4.1341e+00   1.0000e-01
  170  00:00:06   2.1548e+02     30          1.3546e-04   0.0000e+00   1.5226e+02   0.0000e+00   1.1410e-02   3.2128e-03   2.3697e-01  -5.7063e+00   1.0000e-01
  173  00:00:06   2.1548e+02     31  SN      1.2081e-04   0.0000e+00   1.5226e+02   0.0000e+00   1.0769e-02   2.8653e-03   2.1546e-01  -5.7490e+00   1.0000e-01
  180  00:00:06   2.1551e+02     32          9.7240e-05   0.0000e+00   1.5228e+02   0.0000e+00   9.7142e-03   2.3079e-03   1.8201e-01  -5.8166e+00   1.0000e-01
  190  00:00:07   2.1584e+02     33          5.7307e-05   0.0000e+00   1.5250e+02   0.0000e+00   7.7712e-03   1.3671e-03   1.2822e-01  -5.9313e+00   1.0000e-01
  200  00:00:07   2.1752e+02     34          1.6892e-05   0.0000e+00   1.5369e+02   0.0000e+00   5.0263e-03   4.1343e-04   7.2203e-02  -6.0694e+00   1.0000e-01
  210  00:00:07   2.1980e+02     35          6.1220e-06   0.0000e+00   1.5530e+02   0.0000e+00   3.6092e-03   1.5505e-04   5.0200e-02  -6.1323e+00   1.0000e-01
  220  00:00:08   2.2256e+02     36          2.5033e-06   0.0000e+00   1.5725e+02   0.0000e+00   2.7166e-03   6.6021e-05   3.7440e-02  -6.1703e+00   1.0000e-01
  230  00:00:08   2.2576e+02     37          1.1286e-06   0.0000e+00   1.5952e+02   0.0000e+00   2.1167e-03   3.1133e-05   2.9082e-02  -6.1955e+00   1.0000e-01
  231  00:00:08   2.2598e+02     38  EP      1.0762e-06   0.0000e+00   1.5967e+02   0.0000e+00   2.0856e-03   2.9774e-05   2.8651e-02  -6.1968e+00   1.0000e-01
Backbone curve along branch point (BP) 12

 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   1.9970e+02      1  EP      0.0000e+00   7.6149e-04   1.4120e+02   0.0000e+00   4.1376e-02   1.4114e-02   1.5579e+00  -3.6984e-02   1.0000e-01
    5  00:00:00   1.9970e+02      2  EP      1.0000e+00   7.6149e-04   1.4120e+02  -8.4889e-03   4.1376e-02   1.4114e-02   1.5579e+00  -3.6984e-02   1.0000e-01

 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                          4.74e-09  2.00e+02    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   1.9970e+02      1  EP     -8.4889e-03   7.6149e-04   1.4120e+02   1.0000e-01   4.1376e-02   1.4114e-02   1.5579e+00  -3.6984e-02   1.0000e+00
   10  00:00:00   2.1021e+02      2         -6.8788e-03   6.7722e-05   1.4863e+02   1.0115e-02   4.1623e-03   1.4870e-03   1.5365e+00  -4.4008e-01   1.0000e+00
   14  00:00:00   2.1054e+02      3  FP     -6.8567e-03   4.6950e-05   1.4886e+02   7.0892e-03   2.9963e-03   1.0361e-03   1.5075e+00  -6.3745e-01   1.0000e+00
   20  00:00:00   2.1104e+02      4         -7.2093e-03   1.8500e-05   1.4921e+02   2.9846e-03   1.4273e-03   4.1137e-04   1.3936e+00  -1.3835e+00   1.0000e+00
   23  00:00:01   2.1109e+02      5  FP     -7.4436e-03   1.0460e-05   1.4925e+02   1.8916e-03   1.0448e-03   2.3279e-04   1.3915e+00  -1.4910e+00   1.0000e+00
   26  00:00:01   2.1112e+02      6  EP     -6.6186e-03   4.0409e-06   1.4927e+02   1.0001e-03   6.4284e-04   8.9962e-05   1.3977e+00  -1.5249e+00   1.0000e+00
Backbone curve along branch point (BP) 16

 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   2.0987e+02      1  EP      0.0000e+00   2.9640e-04   1.4838e+02   0.0000e+00   9.8510e-03   6.4680e-03   5.0311e-01  -2.4159e+00   1.0000e-01
    5  00:00:00   2.0987e+02      2  EP      1.0000e+00   2.9640e-04   1.4838e+02  -1.6810e-03   9.8510e-03   6.4681e-03   5.0318e-01  -2.4158e+00   1.0000e-01

 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                          7.49e-15  2.10e+02    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   2.0987e+02      1  EP     -1.6810e-03   2.9640e-04   1.4838e+02   1.0000e-01   9.8510e-03   6.4681e-03   5.0318e-01  -2.4158e+00   1.0000e+00
   10  00:00:00   2.1105e+02      2         -5.2195e-03   5.9563e-05   1.4922e+02   9.7796e-03   2.5514e-03   1.3245e-03   1.2206e+00  -1.7407e+00   1.0000e+00
   20  00:00:00   2.1112e+02      3         -5.8340e-03   4.4139e-05   1.4926e+02   6.9801e-03   2.1285e-03   9.8255e-04   1.2721e+00  -1.7649e+00   1.0000e+00
   30  00:00:00   2.1127e+02      4         -6.5076e-03   3.2765e-05   1.4937e+02   5.1193e-03   1.7637e-03   7.3102e-04   1.2946e+00  -2.0457e+00   1.0000e+00
   33  00:00:00   2.1152e+02      5  FP     -6.6497e-03   4.2327e-05   1.4954e+02   6.5622e-03   2.1151e-03   9.4777e-04   1.3578e+00  -2.4511e+00   1.0000e+00
   40  00:00:01   2.1196e+02      6         -6.5339e-03   7.3458e-05   1.4985e+02   1.1279e-02   3.5723e-03   1.6557e-03   1.4943e+00  -2.7130e+00   1.0000e+00
   50  00:00:01   2.1760e+02      7         -5.3933e-03   5.6006e-04   1.5382e+02   9.3983e-02   2.8646e-02   1.3633e-02   1.5896e+00  -3.0410e+00   1.0000e+00
   51  00:00:01   2.1791e+02      8  EP     -5.3432e-03   5.9235e-04   1.5405e+02   1.0000e-01   3.0203e-02   1.4473e-02   1.5907e+00  -3.0424e+00   1.0000e+00
Backbone curve along branch point (BP) 21

 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   2.1132e+02      1  EP      0.0000e+00   3.6216e-04   1.4941e+02   0.0000e+00   5.8688e-03   8.0821e-03   1.6304e+00  -1.5915e+00   1.0000e-01
    1  00:00:00   2.1132e+02      2  BP      6.1483e-08   3.6216e-04   1.4941e+02  -1.5673e-10   5.8688e-03   8.0821e-03   1.6304e+00  -1.5915e+00   1.0000e-01
    5  00:00:00   2.1132e+02      3  EP      1.0000e+00   3.6216e-04   1.4941e+02  -2.5491e-03   5.8690e-03   8.0820e-03   1.6304e+00  -1.5915e+00   1.0000e-01

 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                          1.46e-14  2.11e+02    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   2.1132e+02      1  EP     -2.5491e-03   3.6216e-04   1.4941e+02   1.0000e-01   5.8690e-03   8.0820e-03   1.6304e+00  -1.5915e+00   1.0000e+00
   10  00:00:00   2.1154e+02      2         -3.4898e-03   1.7428e-04   1.4956e+02   3.6005e-02   4.3727e-03   3.9037e-03   1.8340e+00  -1.5731e+00   1.0000e+00
   11  00:00:00   2.1156e+02      3  FP     -3.4945e-03   1.7213e-04   1.4958e+02   3.5391e-02   4.3945e-03   3.8569e-03   1.8552e+00  -1.5669e+00   1.0000e+00
   16  00:00:00   2.1180e+02      4  HB     -3.1673e-03   1.8400e-04   1.4974e+02   3.9027e-02   5.1967e-03   4.1370e-03   2.0687e+00  -1.4424e+00   1.0000e+00
   20  00:00:00   2.1249e+02      5  EP     -1.8356e-03   3.2559e-04   1.5023e+02   1.0000e-01   9.6445e-03   7.3919e-03   2.5034e+00  -9.3877e-01   1.0000e+00
Backbone curve along branch point (BP) 24

 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   2.1249e+02      1  EP      0.0000e+00   3.2559e-04   1.5023e+02   0.0000e+00   9.6445e-03   7.3919e-03   2.5034e+00  -9.3877e-01   1.0000e-01
    1  00:00:00   2.1249e+02      2  BP      6.1494e-08   3.2559e-04   1.5023e+02  -1.1288e-10   9.6445e-03   7.3919e-03   2.5034e+00  -9.3877e-01   1.0000e-01
    5  00:00:00   2.1249e+02      3  EP      1.0000e+00   3.2559e-04   1.5023e+02  -1.8356e-03   9.6445e-03   7.3919e-03   2.5034e+00  -9.3877e-01   1.0000e-01

 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                          5.69e-08  2.12e+02    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   2.1249e+02      1  EP     -1.8356e-03   3.2559e-04   1.5023e+02   1.0000e-01   9.6445e-03   7.3919e-03   2.5034e+00  -9.3877e-01   1.0000e+00
    5  00:00:00   2.1180e+02      2  HB     -3.1674e-03   1.8400e-04   1.4974e+02   3.9027e-02   5.1967e-03   4.1370e-03   2.0687e+00  -1.4424e+00   1.0000e+00
    8  00:00:00   2.1156e+02      3  FP     -3.4945e-03   1.7213e-04   1.4958e+02   3.5391e-02   4.3945e-03   3.8569e-03   1.8552e+00  -1.5669e+00   1.0000e+00
   10  00:00:00   2.1145e+02      4         -3.3323e-03   1.9903e-04   1.4950e+02   4.3254e-02   4.4859e-03   4.4518e-03   1.7423e+00  -1.5887e+00   1.0000e+00
   17  00:00:00   2.1132e+02      5  EP     -2.5491e-03   3.6216e-04   1.4941e+02   1.0000e-01   5.8690e-03   8.0820e-03   1.6304e+00  -1.5915e+00   1.0000e+00
Backbone curve along branch point (BP) 26

 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   2.1791e+02      1  EP      0.0000e+00   5.9235e-04   1.5405e+02   0.0000e+00   3.0203e-02   1.4473e-02   1.5907e+00  -3.0424e+00   1.0000e-01
    1  00:00:00   2.1791e+02      2  BP      6.1467e-08   5.9235e-04   1.5405e+02  -3.2843e-10   3.0203e-02   1.4473e-02   1.5907e+00  -3.0424e+00   1.0000e-01
    5  00:00:00   2.1792e+02      3  EP      1.0000e+00   5.9235e-04   1.5405e+02  -5.3432e-03   3.0203e-02   1.4473e-02   1.5907e+00  -3.0424e+00   1.0000e-01

 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                          1.52e-10  2.18e+02    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   2.1791e+02      1  EP     -5.3432e-03   5.9235e-04   1.5405e+02   1.0000e-01   3.0203e-02   1.4473e-02   1.5907e+00  -3.0424e+00   1.0000e+00
   10  00:00:00   2.1188e+02      2         -6.5583e-03   6.7840e-05   1.4979e+02   1.0421e-02   3.2889e-03   1.5273e-03   1.4788e+00  -2.6844e+00   1.0000e+00
   16  00:00:00   2.1152e+02      3  FP     -6.6497e-03   4.2326e-05   1.4954e+02   6.5621e-03   2.1150e-03   9.4775e-04   1.3578e+00  -2.4511e+00   1.0000e+00
   20  00:00:00   2.1134e+02      4         -6.5890e-03   3.3856e-05   1.4942e+02   5.2855e-03   1.7940e-03   7.5613e-04   1.3027e+00  -2.1890e+00   1.0000e+00
   30  00:00:01   2.1109e+02      5         -5.6335e-03   4.8789e-05   1.4925e+02   7.7914e-03   2.2592e-03   1.0857e-03   1.2584e+00  -1.7493e+00   1.0000e+00
   40  00:00:01   2.1102e+02      6         -4.9647e-03   6.7020e-05   1.4919e+02   1.1245e-02   2.7509e-03   1.4896e-03   1.1909e+00  -1.7466e+00   1.0000e+00
   50  00:00:01   2.1018e+02      7         -2.0781e-03   2.3639e-04   1.4860e+02   6.7730e-02   7.9061e-03   5.1845e-03   6.0928e-01  -2.2778e+00   1.0000e+00
   52  00:00:01   2.0987e+02      8  EP     -1.6810e-03   2.9640e-04   1.4838e+02   1.0000e-01   9.8510e-03   6.4681e-03   5.0318e-01  -2.4158e+00   1.0000e+00

timings = 

  struct with fields:

    dof1: 34.2119
    dof2: 35.1957

Published with MATLAB® R2023a