wolf_3dlyapunov.m

基于Wolf方法计算Lyapunov指数

function lyapunov=wolf_3Dlyapunov(t,Y)
%   用wolf方法求三维实验数据最大李雅普洛夫指数
%
%   输入：演化时间间隔t，3维数据Y(:,1:3)
%   输出：lyapunov指数
 
lyapunov=0;
YL=length(Y);
 
%   不同的系统以下两个参数可能要适当的改变
MaxFL=0.5;
MaxEL=2.5;
% MaxFL=0.05;
% MaxEL=2;
 
fiducial1=1;
fiducial2=3;
for i=4:YL
    if (sum(abs(Y(fiducial1,:)-Y(i,:)))<MaxFL)
        fiducial2=i;
        break;
    end
end
evolveStep=1;
L1=norm(Y(fiducial1,:)-Y(fiducial2,:));
L2=norm(Y(fiducial1+evolveStep,:)-Y(fiducial2+evolveStep,:));
while (1)
    if (fiducial1+evolveStep==YL)||(fiducial2+evolveStep==YL)
        lyapunov=lyapunov+log(L2/L1);
        fiducial1=fiducial1+evolveStep;
        break;
    elseif L2>MaxEL
        lyapunov=lyapunov+log(L2/L1);
        fiducial1=fiducial1+evolveStep;
        fiducial2=fiducial2+evolveStep;
        fiducial2=findreplace(Y,fiducial1,fiducial2,MaxFL);
        evolveStep=1;
        L1=norm(Y(fiducial1,:)-Y(fiducial2,:));
    else
        evolveStep=evolveStep+1;
    end    
    L2=norm(Y(fiducial1+evolveStep,:)-Y(fiducial2+evolveStep,:));
end
fiducial1=fiducial1-1;
lyapunov=lyapunov/(t*fiducial1);
 
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