Lyapunov exponent function submitted by community

It seems this funcftion only takes Ordinary Differential Equations (ODE). I have experimental data. how can I use it with data, instead of ODE

[Sam Chak]

I'm trying to comprehend. Shouldn't your title be revised to "How to obtain Lyapunov exponent from experimental time series?"?

[Walter Roberson]

https://www.mathworks.com/help/predmaint/ref/lyapunovexponent.html

[Jan]

Do you mean a specific function in the FileExchange? If so, which one?

[Walter Roberson]

Probably https://www.mathworks.com/matlabcentral/fileexchange/4628-calculation-lyapunov-exponents-for-ode which is just one of the Lyapunov calculators in the File Exchange.

[Walter Roberson]

https://ideas.repec.org/c/boc/bocode/t741502.html

https://m.youtube.com/watch?v=I4rscPXUYFk

http://freesourcecode.net/matlabprojects/60648/calculates-full-spectrum-of-lyapunov-exponents-or-k-first-exponents--in-matlab

[Torsten]

@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]

Thank you Thank you Thank you I think this might get it

Answer 1

[Sam Chak]

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)