lorenz_lyapunov.m

lorenz_lyapunov 用于混沌动力学的计算

clear;close all;
space=0.01;m=5;tau=11;
X0=[3.0;4.0;5.0];[t,x]=ode45('DYdt',[0:space:100],X0);
x=x(8001:end,1);N=length(x);

k=N-(m-1)*tau;
for i=1:m
    for j=1:k
        y(i,j)=x(j+(i-1)*tau);
    end
end
T=[];
for i=1:5:60
    D=[];
    for j=1:100
        dist=[];
        f=[1:j-1 j+1:k];
        for u=1:length(f)
            d1=norm(y(:,j)-y(:,f(u)),2);
            dist=[dist d1];
        end
        index=f(find(dist==min(dist)));
        if ((j+i)<k)&((index+i)<k)
            d=norm(y(:,j+i)-y(:,index+i),2)/norm(y(:,j)-y(:,index),2);
            D=[D d];
        end
    end
    T=[T;[i*space mean(log(D))]];       
end
plot(T(:,1),T(:,2),'.');xlabel('Time(s)');ylabel('<ln(divergence)>');
lsline
beta = polyfit(T(:,1),T(:,2),1);
lamda=beta(1);