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Fractional-order attractors synthesis via parameter switchings

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Marius-F. Danca, Kai Diethelm

Editorial: Elsevier, Elsevier, Communications in Nonlinear Science and Numerical Simulations, 15, p.3745–3753, 2010.

Rezumat:

In this paper 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 L¨u 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.

Cuvinte cheie: fractional differential equation, Caputo derivative, fractional L¨u system,chaotic attractor, numerical methods