SSM_CONT_PO

Contents

function varargout = SSM_cont_po(obj,type,oid,run,lab,initsol,parName,parRange,outdof,varargin)
        

SSM_CONT_PO

This function performs continuation of periodic orbits of slow dynamics. Each periodic orbit corresponds to a torus (quasi-periodic) response in regular time dynamics.

FRCIRS = SSM_CONT_PO(OBJ,TYPE,OID,RUN,LAB,INITSOL,PARNAME,PARRANGE,OUTDOF,VARARGIN)

See also: SSM_EP2HB, SSM_PO2PO

continuation of equilibrium points in reduced dynamics

prob  = coco_prob();
prob  = cocoSet(obj.contOptions,prob);
bif   = false; % true for SN/PD/TR
runid = coco_get_id(oid, 'po');
switch type
    case 'isol'
        % continuation from an initial periodic solution guess
        [~, data] = ep_read_solution('', coco_get_id(run, 'ep'), lab);
        t0 = initsol.t;
        x0 = initsol.x;
        p0 = [initsol.om;initsol.eps];
        prob = ode_isol2po(prob, '', data.fhan, data.dfdxhan, data.dfdphan, ...
          t0, x0, data.pnames, p0);
        fprintf('\n Run=''%s'': Continue periodic orbits with initial solution.\n', ...
          runid);
    case 'HB'
        % continuation from a Hopf bifurcation fixed point
        prob = ode_HB2po(prob, '', coco_get_id(run, 'ep'), lab);
        fprintf('\n Run=''%s'': Continue periodic orbits born from a HB point with label %d of run %s.\n', ...
          runid, lab, run);
    case 'BP'
        % continuation along a secondary branch passing a branch point
        prob = ode_BP2po(prob, '', coco_get_id(run, 'po'), lab);
        fprintf('\n Run=''%s'': Continue periodic orbits along secondary branch of solution with label %d of run %s.\n', ...
          runid, lab, run);
    case 'po'
        % continuation from a saved periodic solution
        prob = ode_po2po(prob, '', coco_get_id(run, 'po'), lab);
        fprintf('\n Run=''%s'': Continue periodic orbits born from saved solution with label %d of run %s.\n', ...
          runid, lab, run);
    case 'SN'
        % continuation of saddle-node bifurcation periodic orbit
        prob = ode_po2SN(prob, '', coco_get_id(run, 'po'), lab);
        bif  = true;
        fprintf('\n Run=''%s'': Continue SN periodic orbits from label %d of run %s.\n', ...
          runid, lab, run);
    case 'PD'
        % continuation of period-doubling bifurcation periodic orbit
        prob = ode_po2PD(prob, '', coco_get_id(run, 'po'), lab);
        bif  = true;
        fprintf('\n Run=''%s'': Continue PD periodic orbits from label %d of run %s.\n', ...
          runid, lab, run);
    case 'TR'
        % continuation of torus bifurcation periodic orbit
        prob = ode_po2TR(prob, '', coco_get_id(run, 'po'), lab);
        bif  = true;
        fprintf('\n Run=''%s'': Continue TR periodic orbits from label %d of run %s.\n', ...
          runid, lab, run);
    otherwise
        error('type should be selected from {isol,HB,BP,PO,SN,HB}');
end

% read data
fdata = coco_get_func_data(prob, 'po.orb.coll', 'data');
% extract data to fdata.fhan, namely, @(z,p)ode_2mDSSM(z,p,fdata)
odedata = functions(fdata.fhan);
odedata = odedata.workspace{1};
fdata   = odedata.fdata;
m       = numel(fdata.mFreqs);
order    = fdata.order;
ispolar  = fdata.ispolar;
iNonauto = fdata.iNonauto;
rNonauto = fdata.rNonauto;
kNonauto = fdata.kNonauto;
modes    = fdata.modes;
mFreqs   = fdata.mFreqs;
dim      = 2*m;
wdir     = fullfile(pwd,'data','SSM.mat');
SSMcoeffs = load(wdir);
SSMcoeffs = SSMcoeffs.SSMcoeffs;
W_0 = SSMcoeffs.W_0;
W_1 = SSMcoeffs.W_1;
clear('SSMcoeffs');
Nonauto = struct();
Nonauto.iNonauto = iNonauto;
Nonauto.rNonauto = rNonauto;
Nonauto.kNonauto = kNonauto;

% setup continuation arguments
isuniform = false;
if ~bif
    switch parName
        case 'freq'
            isomega = true;
            cont_args = {'om', 'po.period', 'eps'};
        case 'amp'
            isomega = false;
            cont_args = {'eps', 'po.period', 'om'};
        otherwise
            error('Continuation parameter should be freq or amp');
    end

    if ~isempty(obj.FRCOptions.parSamps)
        if isomega
            prob = coco_add_event(prob, 'PS','om',obj.FRCOptions.parSamps);
        else
            prob = coco_add_event(prob, 'PS','eps',obj.FRCOptions.parSamps);
        end
    end

    if strcmp(obj.FRCOptions.sampStyle, 'uniform')
        isuniform = true;
        if isomega
            nOmega = obj.FRCOptions.nPar;
            omSamp = linspace(parRange(1),parRange(2), nOmega);
            prob   = coco_add_event(prob, 'UZ', 'om', omSamp);
        else
            nEpsilon = obj.FRCOptions.nPar;
            epSamp = linspace(parRange(1),parRange(2), nEpsilon);
            prob   = coco_add_event(prob, 'UZ', 'eps', epSamp);
        end
    end
else
    cont_args = {'om', 'eps', 'po.period'};
    isomega = [];
end

% coco run
coco(prob, runid, [], 1, cont_args, parRange);
        

extract results of reduced dynamics at sampled frequencies

FRC = po_reduced_results(runid,ispolar,isomega,mFreqs,obj.FRCOptions.nt,isuniform);
        

map torus back to physical system

if isempty(isomega)
    isomega = true;
end
fprintf('\n FRCs from =''%s'': generating torus in physical domain.\n', ...
    runid);
FRCdata = struct();        FRCdata.isomega = isomega;
FRCdata.mFreqs  = mFreqs;  FRCdata.order  = order;
FRCdata.ispolar = ispolar; FRCdata.modes  = modes;   FRCdata.dim = dim;
FRC = FRC_reduced_to_full(obj,Nonauto,'po',FRC,FRCdata,W_0,W_1,outdof,varargin{:});
varargout{1} = FRC;
% write results to hard driver
fdir = fullfile(pwd,'data',runid,'SSMpo.mat');
save(fdir, 'FRC');
        

end
        

Published with MATLAB® R2023a