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Zbl 1222.37107
Danca, Marius F.; Diethelm, Kai
Fractional-order attractors synthesis via parameter switchings. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 15, No. 12, 3745-3753 (2010). ISSN 1007-5704

Summary: We provide numerical evidence, via graphics generated with the help of computer simulations, that switching the control parameter of a dynamical system belonging to a class of fractional-order systems in a deterministic way, one obtains an attractor which belongs to the class of all admissible attractors of the considered system. For this purpose, while a multistep numerical method for fractional-order differential equations approximates the solution to the mathematical model, the control parameter is switched periodically every few integration steps. The switch is made inside of a considered set of admissible parameter values. Moreover, the synthesized attractor matches the attractor obtained with the control parameter replaced with the averaged switched parameter values. The results are verified in this paper on a representative system, the fractional-order Lü system. In this way we were able to extend the applicability of the algorithm presented in earlier papers using a numerical method for fractional differential equations.

MSC 2000:: *37N35 Dynamical systems in control
34A08
37D45 Strange attractors, chaotic dynamics
26A33 Fractional derivatives and integrals (real functions)
37C70 Attractors and repellers, topological structure

Keywords: fractional differential equation; Caputo derivative; fractional Lü system; chaotic attractor; numerical methods

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