computeroflyapnov.m

分形计算的几个程序原码

%二维Henon映射的Lyapunov指数的计算
%The computation of Lyapunov exponent for two-dimension Henon maping
%关键词：Henon映射，Lyapunov指数
%keywords: Henon maping, Lyapunov exponent 

%Henon maping of two dimension:
%x(n+1)=1-1.4.*x(n).^2+y(n);
%y(n+1)=0.3.*x(n);

%Jacobi matrix for Henon maping:
%J=[-2.8.*x(n),1;0.3,0]


%The program MATLAB as following:

% The computation of Lyapunov for two-dimension Henon maping
% reference:
% 岳毅宏，韩文秀，基于系统Lyapunov指数分析的倍周期分岔研究，
% 控制与决策，17，2002: 814-819
clc;clear;close all;
% rand('state',0);
% Author's email:[e-mail]
% \copyright:zjliu
M=1000;
N=1000;
D2=1;
D3=0.3;
D4=0;
L1=0;
L2=0;
q=1;
for k=1:M;
    x=zeros(1,N);
    y=zeros(1,N);
    x(1)=rand;
    y(1)=rand;
    for L=1:N-1;
        x(L+1)=1-1.4.*x(L)^2+y(L);
        y(L+1)=0.3*x(L);
    end
    if abs(x(end))<2;
        D1=-2.8*x(end);
        JT=[D1,D2;D3,D4];
        [v,d]=eig(JT);
        d=diag(d);
        L1=L1+log(abs(d(1))); % the first Lyapunonv exponent
        L2=L2+log(abs(d(2))); % the second Lyapunonv exponent
        Xp(q)=x(end);
        Yp(q)=y(end);
        q=q+1;
    end
end
% display the first and second Lyapunonv exponent
L1=L1/(q-1),
L2=L2/(q-1),
% Draw figure for Henon maping:
figure; plot(Xp,Yp,'k.','markersize',5);