Contents
Initialize continuation of equilibrium bifurcation (fold or Hopf)
function [bifbranch,suc]=SetupStstBifurcation(funcs,branch,ind,type,varargin)
Inputs
- funcs: functions used for DDE
- branch: branch of stst along which bifurcation was discovered
- ind: index of approximate bifurcation point
- type: tpye of bifurcation, string: at the moment either 'fold' or 'hopf'
Important name-value pair inputs
- 'contpar' (integers default []): index of continuation parameters (replacing free pars of branch)
- 'correc' (logical, default true): apply p_correc to first points on bifurcation branch
- 'dir' (integer, default []): which parameter to vary initially along bifurcation branch (bifbranch has only single point if dir is empty)
- 'step' (real, default 1e-3): size of initial step if dir is non-empty
All other named arguments are passed on to fields of bifbranch
Outputs
- bifbranch: branch of bifurcation points with first point (or two points)
- suc: flag whether corection was successful
Parameter limits for bifbranch etc are inherited from branch, unless overridden by optional input arguments.
process options
default={'contpar',[],'correc',true,'dir',[],'step',1e-3,'excludefreqs',[]};
[options,pass_on]=dde_set_options(default,varargin,'pass_on');
% initialize branch of bifurcations (bifbranch)
bifbranch=branch;
bifbranch=replace_branch_pars(bifbranch,options.contpar,pass_on);
point=branch.point(ind);
if ~isfield(point,'stability') || isempty(point.stability)
point.stability=p_stabil(funcs,point,branch.method.stability);
end
create initial guess for correction
switch type case 'hopf' pini0=p_tohopf(funcs,point,options.excludefreqs); case 'fold' pini0=p_tofold(funcs,point); otherwise warning('SetupStstBifurcation:type',... 'SetupStstBifurcation: type %s not supported',type); suc=0; return end
correct and add 2nd point if desired
[bifbranch,suc]=correct_ini(funcs,bifbranch,pini0,...
options.dir,options.step,options.correc);
end