Initialize continuation of Fold bifurcations

Inputs
Outputs
process options
set up functions of extended system
create initial guess for correction
correct and add 2nd point if desired

function [foldbranch,suc]=SetupFold(funcs,branch,ind,varargin)

Inputs

funcs: functions used for DDE
branch: branch of stst along which Fold was discovered
ind: index of approximate Fold point

Important optional inputs (name-value pairs) outputs foldbranch: Fold branch with first point (or two points) suc: flag whether corection was successful

Important name-value pair inputs

'contpar' (integers default []): index of additional continuation parameters (in addition to free pars of branch
'correc' (logical, default true): apply p_correc to first points on fold branch
'dir' (integer, default []): which parameter to vary initially along fold branch (foldbranch 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 foldbranch

Outputs

foldbranch: Hopf branch with first point (or two points)
suc: flag whether corection was successful

process options

default={'contpar',[],'correc',true,'dir',[],'step',1e-3};
[options,pass_on]=dde_set_options(default,varargin,'pass_on');
% initialize branch of folds (pbranch)
foldbranch=df_brnch(funcs,options.contpar,'fold');
foldbranch.method.point=branch.method.point;
foldbranch.method.continuation=dde_set_options(foldbranch.method.continuation,pass_on,'pass_on');
foldbranch.method.point=dde_set_options(foldbranch.method.point,pass_on,'pass_on');
foldbranch.method.stability=dde_set_options(foldbranch.method.stability,pass_on,'pass_on');
if isempty(options.contpar)
    % if no continuation parameters are given use free parameters of branch
    foldbranch.parameter.free=branch.parameter.free;
elseif length(options.contpar)==1;
    % if single continuation parameter is given prepend to free parameters of branch
    foldbranch.parameter.free=[options.contpar,branch.parameter.free];
else
    foldbranch.parameter.free=options.contpar(:)';
end
foldbranch.parameter=dde_set_options(foldbranch.parameter,pass_on,'pass_on');
point=branch.point(ind);
if ~isfield(point,'stability')
    point.stability=p_stabil(funcs,point,branch.method.stability);
end

set up functions of extended system

create initial guess for correction

foldini0=p_tofold(funcs,point);

correct and add 2nd point if desired

[foldbranch,suc]=correct_ini(funcs,foldbranch,foldini0,...
    options.dir,options.step,options.correc);

end