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FO_Lyapunov_p

version 1.0.3 (3.39 KB) by Marius-F. Danca
Program to compute LEs as function of p of autonomous systems of commensurate Caputo's Fractional Order

9 Downloads

Updated 8 Jul 2022

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**slight chnages**
The program, FO_Lyapunov_p, can be used either alone to determined the LEs of a FO system for a fixed fractional order p (see e.g. LE_RF_p.m which contains the extended system), or can be used to obtain the evolution of LEs as function of p, case when the code run_FO_LE_p must be used.
  1. To obtain the LEs for a given p, one uses
LE=FO_Lyapunov_p(ne,ext_fcn,t_start,h_norm,t_end,x_start,h,q,p);
For example, for the RF system [1]
LE=FO_Lyapunov_p(3,@LE_RF_p,0,0.02,200,[0.1;0.1;0.1],0.02,0.998,1.3)
2. If one intends to obtain the evolution of LEs as function of p one uses
run_LE_FO_p(ne,ext_fcn,t_start,h_norm,t_end,x_start,h,q,p_min,p_max,n);
E.g., for the same system RF
run_LE_FO_p(3,@LE_RF_p,0,0.02,200,[0.1;0.1;0.1],0.02,0.998,1.1,1.3,800)
Note that FO_Lyapunov_p.m, LE_RF_p.m, run_FO_LE_p and FDE12.m (used 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 (e.g. h=0.002 and h_norm=0.2, but to the detriment of computational time)
[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_p (https://www.mathworks.com/matlabcentral/fileexchange/114610-fo_lyapunov_p), 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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