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A toolbox for finding horseshoes in 2D maps

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24 Feb 2007 (Updated )

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

simuodeSprt.m
function simuode
clc;
x0=[1;1;0];a=0;
op = odeset('RelTol',1e-6,'AbsTol',1e-6,'Events',@events);
[t,x,te,xe,ie] = ode45(@odefun,[0,200],x0,op,a);
figure;plot3(x(:,1),x(:,2),x(:,3),'b-');hold on;
plot3(xe(:,1),xe(:,2),xe(:,3),'r.');
grid on;xlabel('x');ylabel('y');
axis equal;

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 = 0;% Ƿvalue==0ʱֹ㷨
direction  = 1; % valueı仯 ɣ䣭direction1֮10

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