how to find lyapunov exponent of 3d discrete system

for example 3 species predator-prey model

Answer 1

[Rahul]

Hi @itendra k kumar,

I understand that you require to find the Lyapunov exponent of a 3d discrete system.

MATLAB offers a 'lyapunovExponent' function which would be useful in this case.

Here is an example code for your reference:

% Define the predator-prey model as a function handle - this is an example,
% you can define your own model according to your specifications.
predator_prey = @(x, params) [
    x(1) * (1 + params(1) - params(2) * x(3));
    x(2) * (1 + params(1) - params(2) * x(3));
    x(3) * (1 - params(3) + params(2) * (x(1) + x(2)))
];

% I have assumed 'params' and 'x' to be the variables required to define
% the predator-prey model.

% This 'predator-prey' model can be used as the data to find the 'Lyapunov
% Exponent'
LE = lyapunovExponent(predator_prey, fs, dim);

You can refer to the following MATLAB documentations to know more:

'lyapunovExponent': https://www.mathworks.com/help/releases/R2022a/predmaint/ref/lyapunovexponent.html

'Solve Prey-Predator Equations': https://www.mathworks.com/help/releases/R2022a/matlab/math/numerical-integration-of-differential-equations.html

Hope this helps! Thanks.