image thumbnail

A toolbox for finding horseshoes in 2D maps

by

 

24 Feb 2007 (Updated )

This GUI programe presents an efficient method for finding topological horseshoes in chaotic systems

rtmapSprt.m
function [xr,varargout]=rtmapSprt(varargin)
a=-0.000;
iro=[1;2];
op = odeset('RelTol',1e-6,'AbsTol',1e-6,'Events',@events);
if nargin==1
    x0=varargin{1};
else
    x0=[1;1];
end
xe=[x0(1);x0(2);0];
[t,x] = ode45(@odefun,[0,1e-5],xe,[],a);
[t,x,te,xe,ie] = ode45(@odefun,[0,200],x(end,:)',op,a);
xr=xe(end,iro)';
if nargout>1
    varargout{1}=1;
end

function dx=odefun(t,x,a)
dx=[x(2)*x(3)+a;x(1)*x(1)-x(2);1-4*x(1)];

function [value,isterminal,direction] = events(t,x,a)
value = x(3); % ʱ䷢ıʽ
isterminal = 1;% Ƿvalue==0ʱֹ㷨
direction  = 1; % valueı仯 ɣ䣭direction1֮10

Contact us