Lyapunov exponent function submitted by community

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Don
Don 2022-6-14
回答： Sam Chak 2022-6-18
It seems this funcftion only takes Ordinary Differential Equations (ODE). I have experimental data. how can I use it with data, instead of ODE
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Torsten
Torsten 2022-6-15
编辑：Torsten 2022-6-15
@Don comment moved here:
Were gaining on it!
The function i'm interested in has been submitted by the COMMUNITY:
MathWorks FileExchange website for community implementations of Lyapunov Exponent calculations. https://www.mathworks.com/matlabcentral/fileexchange/4628-calculation-lyapunov-exponents-for-ode
However, this one apparently works with ODE
I have experimental data. I need one that works with a data file. There is one in the Predictive Maintenance Toolbox, but that costs a lot of money and I have no use for the rest of the toolbox.
is tit possible to find a community supplied function that will work with data??
Don
Don 2022-6-15
Thank you Thank you Thank you I think this might get it

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Sam Chak
Sam Chak 2022-6-18
Ran in:
Hi @Don
If your experimental data is not large, then you can test lyapunovExponent() here to see if it works for your case.
https://www.mathworks.com/help/predmaint/ref/lyapunovexponent.html
% Parameters
sigma = 10;
beta = 8/3;
rho = 28;
% Lorenz System
f = @(t, x) [-sigma*x(1) + sigma*x(2); ...
rho*x(1) - x(2) - x(1)*x(3); ...
-beta*x(3) + x(1)*x(2)];
tspan = linspace(0, 88, 8801);
init = [1 1 1];
[t, x] = ode45(f, tspan, init);
plot3(x(:,1), x(:,2), x(:,3)), view(45, 30)
% Characterize the rate of separation of infinitesimally close trajectories
xdata = x(:,1);
fs = 10;
dim = 3;
[~, lag] = phaseSpaceReconstruction(xdata, [], dim);
eRange = 50;
lyapunovExponent(xdata, fs, lag, dim, 'ExpansionRange', eRange)

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