set_rot_funcs - Fill in funcs structure for use with DDE-Biftool, rotational symmetric case

Contents

function funcs=set_rotfuncs(varargin)

Named arguments

See rotsym_demo for example usage uses defaults df_deriv for partial derivatives

(c) DDE-BIFTOOL v. 3.1.1(30), 15/04/2014

Process options

defaults={'rotation',[],'exp_rotation',[],'rot_tol',1e-8,'hjac',1e-6};
[options,pass_on]=dde_set_options(defaults,varargin,'pass_on');
rot_tol=options.rot_tol;
funcs=set_funcs(pass_on{:});

check rotation matrices

if isempty(options.rotation)
    error('rotation matrix must be given as argument ''rotation''');
else
    funcs.rotation=options.rotation;
end
if isempty(options.exp_rotation)
    funcs.exp_rotation=@(phi)expm(funcs.rotation*phi);
else
    funcs.exp_rotation=options.exp_rotation;
end
% test comaptibility
phi=linspace(0,2*pi,10);
for i=1:length(phi)
    err=expm(funcs.rotation*phi(i))-funcs.exp_rotation(phi(i));
    if max(abs(err))>rot_tol
        error('exp(rot*phi)~=exp_rotation(phi) for phi=%g',phi(i));
    end
end
err=funcs.exp_rotation(2*pi)-eye(size(funcs.rotation));
if max(abs(err))>rot_tol
    error('exp(rot*2*pi)~=Id');
end
err=funcs.rotation+funcs.rotation.';
if max(abs(err))>rot_tol
    error('rot~=-rot^T');
end

modify sys_rhs to include shift to rotating coordinates

funcs.orig_rhs=funcs.sys_rhs;
funcs.sys_rhs=@(xx,p)rot_rhs(xx,p,funcs.rotation,funcs.exp_rotation,...
    funcs.orig_rhs,funcs.sys_tau,funcs.x_vectorized);

set derivatives to defaults if not given by user

if ~funcs.sys_deri_provided;
    funcs.orig_deri=funcs.sys_deri;
    funcs.sys_deri=@(x,p,nx,np,v)df_deriv(funcs,x,p,nx,np,v,options.hjac);
else
    %funcs.orig_deri=funcs.sys_deri;
    %funcs.sys_deri=@(x,p,nx,np,v)rot_deriv(funcs,x,p,nx,np,v);
    error('No support yet for passing on user-defined derivatives.');
end

modify sys_cond to include fixing of rotational phase

funcs.orig_cond=funcs.sys_cond;
funcs.sys_cond=@(p)rot_cond(p,funcs.rotation,funcs.orig_cond);

state-dependent delays currently not supported

if funcs.tp_del
    error('State-dependent delays are not supported.')
end
if isempty(funcs.sys_dtau) % unused
    funcs.sys_dtau=@(x,p,nx,np,v)df_derit(funcs,x,p,nx,np,v);
end

end

Published with MATLAB® 7.14