## Code for noncommensurate fractional-order Lyapunov exponents

version 1.0.1 (3.18 KB) by
The program prints and plots the Lyapunov exponents of noncommensurate fractional order as function of time.

Updated 14 Jun 2021

The code, FO_NC_Lyapunov.m, determines all Lyapunov exponents for a class of noncommensurate fractional-order systems modeled by Caputo's derivative, following the Benettin–Wolf algorithm. The program continues the matlab code for Lyapunov exponents of commensurate fractional order presented in
 Marius-F. Danca, Nikolay Kuznetsov, Matlab code for Lyapunov exponents of fractional order systems, IJBC, 28(05), 1850067 (2018)
https://www.mathworks.com/matlabcentral/fileexchange/77939-matlab-code-for-lyapunov-exponents-of-fractional-order
Like the previous code, it uses an existing Matlab program for Lyapunov exponents of integer order, lyapunov.m, via a fast routine for differential equations of noncommensurate order, fde_pi12_pc.m.
How to use it:
[t,LE]=FO_NC_Lyapunov(ne,ext_fcn,t_start,h_norm,t_end,x_start,h,q,out);
where:
ne - system dimension;
ext_fcn - function containing the extended system of FO (see e.g. LE_RF.m in  or );
t_start, t_end - time span (fde_pi12_pc);
h_norm - step for Gram-Schmidt renormalization;
x_start - initial condition;
h - integration step for fde_pi12_pc;
q=[q_1,q_2,...,q_ne] - the fractional order;
out - priniting step of LEs values;
out==0 - no print.
and
t- time values;
LE -Lyapunov exponents to each time value printed every 'out' step
Example:
[t,LE]=FO_NC_Lyapunov(3,@Lorenz_ext,0,.5,1000,[.1,.1,.1]',0.01,[.92,.92,.92],500)
Note that the files FO_NC_Lyapunov, fde_pi12_pc, and ext_fcn (e.g. Lorenz_ext), must be in the same folder
The way in which the code can be used to obtain bifurcation diagrams vs one parameter, order etc, can be deduced from 

### Cite As

Nikolay Kuznetsov (2021). Code for noncommensurate fractional-order Lyapunov exponents (https://www.mathworks.com/matlabcentral/fileexchange/92753-code-for-noncommensurate-fractional-order-lyapunov-exponents), MATLAB Central File Exchange. Retrieved .

Marius-F. Danca, Matlab code for Lyapunov exponents of fractional-order systems, Part II: The non-commensurate case, IJBC, accepted on Jun 12, 2021.

##### MATLAB Release Compatibility
Created with R2021a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux