Lyapunov exponent function submitted by community
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It seems this funcftion only takes Ordinary Differential Equations (ODE). I have experimental data. how can I use it with data, instead of ODE
7 个评论
Sam Chak
2022-6-14
I'm trying to comprehend. Shouldn't your title be revised to "How to obtain Lyapunov exponent from experimental time series?"?
Walter Roberson
2022-6-14
编辑：Jan
2022-6-14
Jan
2022-6-14
Do you mean a specific function in the FileExchange? If so, which one?
Walter Roberson
2022-6-14
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
2022-6-15
编辑：Walter Roberson
2022-6-15
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
@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
2022-6-15
采纳的回答
Hi @Don
If your experimental data is not large, then you can test lyapunovExponent() here to see if it works for your case.
% 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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