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arXiv:2104.11323 (physics)
[Submitted on 8 Apr 2021 (v1), last revised 14 Jun 2021 (this version, v2)]

Title:Matlab code for Lyapunov exponents of fractional-order systems, Part II: The non-commensurate case

Authors:Marius-F. Danca
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Abstract:In this paper the Benettin-Wolf algorithm to determine all Lyapunov exponents adapted to a class of non-commensurate fractional-order systems modeled by Caputo's derivative and the corresponding Matlab code are presented. The paper continues the work started in [Danca & Kuznetsov, 2018], where the Matlab code of commensurate fractional-order systems is given. To integrate the extended system, the Adams-Bashforth-Moulton for fractional differential equations is utilized. As the the Matlab program for commensurate-order systems, the program presented in this paper prints and plots all Lyapunov exponents as function of time. The program can be simply adapted to plot the evolution of the Lyapunov exponents as function of orders, or a function of a bifurcation parameter. A special attention is payed to the periodicity of fractional-order systems and its influences. The case of the Lorenz system is considered.
Comments: Accepted (IJBC, 2021)
Subjects: Computational Physics (physics.comp-ph); Chaotic Dynamics (nlin.CD)
Cite as: arXiv:2104.11323 [physics.comp-ph]
  (or arXiv:2104.11323v2 [physics.comp-ph] for this version)
  https://doi.org/10.48550/arXiv.2104.11323
Related DOI: https://doi.org/10.1142/S021812742150187X

Submission history

From: Marius-F. Danca [view email]
[v1] Thu, 8 Apr 2021 16:55:32 UTC (1,605 KB)
[v2] Mon, 14 Jun 2021 07:41:42 UTC (1,620 KB)
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