SSM_CONT_TOR
Contents
function varargout = SSM_cont_tor(obj,type,oid,run,lab,parName,parRange,outdof,varargin)
SSM_CONT_TOR
This function performs continuation of 2D tori of slow dynamics. Each 2D tori corresponds to a 3D torus (quasi-periodic) response in regular time dynamics.
FRCIRS = SSM_TR2TOR(OBJ,OID,RUN,LAB,PARNAME,PARRANGE,OUTDOF,VARARGIN)
oid: runid of current continuation
type: TR/tor/BP
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run: runid of continuation for saved solution
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lab: label of continuation for saved solution, which must be the label of a TR/BP point if type=TR/BP
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parName: freq-amp/amp/freq continuation parameter. In the case of freq-amp, both two parameters are free to change and hence varrho is fixed. In contrast, varrho is fixed if there is only one continuation parameter
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parRange: continuation domain of parameter, which is given in the form of {[om1,om2],[f1,f2]} for freq-amp, [f1,f2] for amp and [om1,om2] for freq. It is noted that the domain [om1,om2] should contain the natural frequency with index 1 in the mFreq vector
outdof: output for dof in physical domain
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varargin: ['saveICs'] flag for saving the initial point in trajectory
See also: SSM_PO2TR, SSM_TOR2PTOR, SSM_CONT_TOR
continuation of equilibrium points in reduced dynamics
prob = coco_prob(); prob = coco_set(prob, 'tor', 'autonomous', true, 'nOmega', 0); prob = cocoSet(obj.contOptions,prob); runid = coco_get_id(oid, 'tor'); switch type case 'TR' prob = ode_TR2tor(prob, '', coco_get_id(run, 'po'), lab,... obj.FRCOptions.torNumSegs, obj.FRCOptions.torRotDiret,... obj.FRCOptions.torPurtb); fprintf('\n Run=''%s'': Continue tori born from TR point with label %d of run %s.\n', ... runid, lab, run); case 'tor' prob = ode_tor2tor(prob, '', coco_get_id(run, 'tor'), lab); fprintf('\n Run=''%s'': Continue tori from label %d of run %s.\n', ... runid, lab, run); case 'BP' prob = ode_BP2tor(prob, '', coco_get_id(run, 'tor'), lab); fprintf('\n Run=''%s'': Continue tori along secondary branch 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, 'tor.bvp.seg1.coll', 'data'); % extract data to fdata.fhan, namely, @(z,p)ode_2mDSSM(z,p,fdata) odedata = functions(fdata.fhan); odedata = odedata.workspace{1}; odedata = functions(odedata.args.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 switch parName case 'freq-amp' % varrho is fixed cont_args = {'om', 'eps', 'om1' ,'om2', 'varrho'}; case 'freq' % varrho is free to vary isomega = true; cont_args = {'om', 'varrho', 'om1', 'om2', 'eps'}; case 'amp' % varrho is free to vary isomega = false; cont_args = {'eps', 'varrho', 'om1', 'om2', 'om'}; otherwise error('Continuation parameter should be freq or amp'); end % coco run coco(prob, runid, [], 1, cont_args, parRange);
extract results of reduced dynamics at sampled frequencies
FRC = tor_reduced_results(runid,ispolar,isomega,mFreqs,obj.FRCOptions.nt);
map torus back to physical system
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,'tor',FRC,FRCdata,W_0,W_1,outdof,varargin{:}); varargout{1} = FRC; % write results to hard driver fdir = fullfile(pwd,'data',runid,'SSMtor.mat'); save(fdir, 'FRC');
end