how to find largest Lyapunov exponent for Lorenz in Rosenstein's Algorithm?

function d = lyarosenstein(x,f,m,tao,meanperiod,maxiter) 
% d:divergence of nearest trajectoires
% x:signal
% tao:time delay
% m:embedding dimension

N=length(x);


% [T, X] = feval(@ode45, @rossler, [1 100 + .01], x);
M=N-(m-1)*tao;
Y=psr_deneme(x,m,tao);
for i=1:M
    
    x0=ones(M,1)*Y(i,:);
    distance=sqrt(sum((Y-x0).^2,2));
    for j=1:M
        if abs(j-i)<=meanperiod
            distance(j)=1e10;
        end
    end
    [neardis(i) nearpos(i)]=min(distance);
end
for k=1:maxiter
    
    maxind=M-k;
    evolve=0;
    pnt=0;
    for j=1:M
        if j<=maxind && nearpos(j)<=maxind
            dist_k=sqrt(sum((Y(j+k,:)-Y(nearpos(j)+k,:)).^2,2));
             if dist_k~=0
                evolve=evolve+log(dist_k);
                pnt=pnt+1;
             end
        end
    end
    if pnt > 0
        d(k)=evolve/pnt;
    else
        d(k)=0;
    end
    
end
figure
plot(log(d))
% LLE Calculation
fs=2000;%sampling frequency
tlinear=15:78;
F = polyfit(tlinear,d(tlinear),1);
lle = F(1)*fs;

function Y=psr_deneme(x,m,tao,npoint)
%Phase space reconstruction
%x : time series 
%m : embedding dimension
%tao : time delay
%npoint : total number of reconstructed vectors
%Y : M x m matrix
% author:"Merve Kizilkaya"
N=length(x);
if nargin == 4
    M=npoint;
else
    M=N-(m-1)*tao;
end
Y=zeros(M,m); 
for i=1:m
    Y(:,i)=x((1:M)+(i-1)*tao)';
end
% 

Answer 1

[SOUMNATH PAUL]

Hi,

Kindly do the following changes to your code to fix the issue:

1. Remove ‘f’ in the lyarosenstein function because we are not going to use it further in the code.
2. You can plot the raw divergence ‘d’ instead of the logarithm of the divergence ‘log(d)’.
3. Include scripts to output the current verbose values which will help you in debugging.

Kindly go through the functions section of the below link for a related example:

https://www.mathworks.com/matlabcentral/fileexchange/38424-largest-lyapunov-exponent-with-rosenstein-s-algorithm

Hope it helps!

Regards,

Soumnath