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FO_Lyapunov_q

version 1.0.2 (3.38 KB) by Marius-F. Danca
Program to compute LEs as function of q, of autonomous systems of commensurate Caputo's Fractional Order

8 Downloads

Updated 8 Jul 2022

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**slight changes**
The program, FO_Lyapunov_q, can be used either alone, to determined the LEs of a FO system for a fixed fractional order q (see e.g. LE_RF.m which contains the extended system), or can be used to obtain the variation of LEs as function of q, case when the code run_FO_LE_q must be used [1].
  1. To obtain the LEs for a given q, for, e.g., RF system, one uses
LE=FO_Lyapunov_q(ne,ext_fcn,t_start,h_norm,t_end,x_start,h,q);
For example, for the RF system [1]
LE=FO_Lyapunov_q(3,@LE_RF,0,0.02,200,[0.1;0.1;0.1],0.02,0.998)
2. If one intends to obtain the evolution of LEs as function of q one uses
run_FO_LE_q(ne,ext_fcn,t_start,h_norm,t_end,x_start,h,q_min,q_max,n)
E.g., for the same system RF
run_FO_LE_q(3,@LE_RF,0,0.02,150,[0.1;0.1;0.1],0.02,0.9,1,800)
Note that FO_Lyapunov_q.m, LE_RF.m, run_FO_LE_q and FDE12.m (necessary to integrate the system) must be in the same folder.
As mentioned in [1], the relation between h_norm and h is essential. Here both are chosen equal (0.02), but multiple of h for h_norm should be tried
[1] Marius-F. Danca and N. Kuznetsov, Matlab code for Lyapunov exponents of fractional order systems, International Journal of Bifurcation and Chaos, 28(05)(2018), 1850067

Cite As

Marius-F. Danca (2022). FO_Lyapunov_q (https://www.mathworks.com/matlabcentral/fileexchange/114605-fo_lyapunov_q), MATLAB Central File Exchange. Retrieved .

Marius-F. Danca and N. Kuznetsov, Matlab code for Lyapunov exponents of fractional order systems, International Journal of Bifurcation and Chaos, 28(05)(2018), 1850067

MATLAB Release Compatibility
Created with R2022a
Compatible with any release
Platform Compatibility
Windows macOS Linux
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