www.pudn.com > Chaos_Prediction.rar > Main_Ikeda.m

%function [x,y]=ikeda(n,mu,x0,y0) 
%Syntax: [x,y]=ikeda(n,mu,x0,y0) 
%_____________________________________ 
% 
% Simulation of the Ikeda map. 
%    x'=1+mu*(xcos(t)-ysin(t) 
%    y'=mu*(xsin(t)+ycos(t)) 
% 
% x and y are the simulated time series. 
% n is the number of the simulated points. 
% mu is the parameter. 
% x0 is the initial value for x. 
% y0 is the initial value for y. 
% 
% 
% Reference: 
% 
% Ikeda K (1979): Multiple-valued stationary state and its instability of the 
% transmitted light by a ring cavity system. Optics Communications 30: 257 
clc 
clear 
close all 
 
n=5000; 
mu=0.9; 
x0=0.1; 
y0=0.1; 
 
 
% Initialize 
t=0.4-6/(1+x0^2+y0^2); 
x(1,1)=1+mu*(x0*cos(t)-y0*sin(t)); 
y(1,1)=mu*(x0*sin(t)+y0*cos(t)); 
 
% Simulate 
for i=2:n 
    t=0.4-6/(1+x(i-1,1)^2+y(i-1,1)^2); 
    x(i,1)=1+mu*(x(i-1,1)*cos(t)-y(i-1,1)*sin(t)); 
    y(i,1)=mu*(x(i-1,1)*sin(t)+y(i-1,1)*cos(t)); 
end 
 
plot(x,y,'.','MarkerSize',1) 
xlabel('x');ylabel('y') 
title('ikeda attractor') 
 
% Add normal white noise 
% level is the noise standard deviation divided by the standard deviation of 
%   the noise-free time series. We assume Gaussian noise with zero mean. 
%x=x+randn(n,1)*level*std(x); 
%y=y+randn(n,1)*level*std(y);