## Matlab code for Lyapunov exponents of fractional order

version 1.0.2 (6.45 KB) by
The code computes all LEs of fractional-order systems of commensurate order (author Marius-F. Danca)

Updated 09 Jul 2020

The code determines all Lyapunov exponents for a class offractional-order systems modeled by Caputo's derivative. The underlying numerical method to solve the extended system of fractional order, composed of the initial value problem and the variational system, is the predictor-corrector Adams-Bashforth-Moulton for fractional differential equations. The program is developed from an existing Matlab program for Lyapunov exponents of integer order. To decrease the computing time, the free fast Matlab routine, FDE12, which implements the Adams-Bashforth-Moulton method, is utilized.

The program can be used to draw also the LEs as function of the bifurcation parameter or as function of the fractional order (see ref)

Usage:

[t,LE]=FO_Lyapunov(ne,@ext_fcn,t_start,h_norm,t_end,x_start,h,q,out);

Input:
ne - system dimension;
ext_fcn - function containing the extended system of FO (here the Rabinovich-Fabrikant system, file 'LE_FO_RF');
t_start, t_end - time span (FDE12);
h_norm - step for Gram-Schmidt renormalization (Lyapunov algorithm);
x_start - initial condition;
h - integration step;
q - the fractional order;
out - printing step of LEs values;
out==0 - no print.

Output:
t - time values;
LE Lyapunov exponents to each time value printed every 'out' step.

The code uses the free routine FDE12 for ABM method
Example of use for the RF system:

[t,LE]=FO_Lyapunov(3,@LE_FO_RF,0,0.02,300,[0.1;0;1;0.1],0.005,0.999,1000);

### Cite As

Marius-F. Danca, Nikolay Kuznetsov, Matlab code for Lyapunov exponents of fractional order systems, International Journal of Bifurcation and Chaos, 28(05), 1850067 (2018). DOI:/10.1142/S0218127418500670

##### MATLAB Release Compatibility
Created with R2020a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux