Theory and applications of new fractional-order chaotic system under Caputo operator

Ndolane Sene

doi:10.11121/ijocta.2022.1108

Authors

Ndolane Sene D´epartement de Math´ematiques de la D´ecision, Facult´e des Sciences Economiques et Gestion, Universit´e Cheikh Anta Diop de Dakar, Dakar Fann, Senegal https://orcid.org/0000-0002-8664-6464

DOI:

https://doi.org/10.11121/ijocta.2022.1108

Keywords:

Phase portraits, Fractional-order chaotic system, Attractors, Lyapunov exponents, Chaotic behavior

Abstract

This paper introduces the properties of a fractional-order chaotic system described by the Caputo derivative. The impact of the fractional-order derivative has been focused on. The phase portraits in different orders are obtained with the aids of the proposed numerical discretization, including the discretization of the Riemann-Liouville fractional integral. The stability analysis has been used to help us to delimit the chaotic region. In other words, the region where the order of the Caputo derivative involves and where the presented system in this paper is chaotic. The nature of the chaos has been established using the Lyapunov exponents in the fractional context. The schematic circuit of the proposed fractional-order chaotic system has been presented and simulated in via Mutltisim. The results obtained via Multisim simulation of the chaotic circuit are in good agreement with the results with Matlab simulations. That provided the fractional operators can be applied in real- worlds applications as modeling electrical circuits. The presence of coexisting attractors for particular values of the parameters of the presented fractional-order chaotic model has been studied.

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Author Biography

Ndolane Sene, D´epartement de Math´ematiques de la D´ecision, Facult´e des Sciences Economiques et Gestion, Universit´e Cheikh Anta Diop de Dakar, Dakar Fann, Senegal

was born in Senegal in 1986. He received a Ph.D degree from Cheikh Anta Diop University in June 2017. He currently works on fractional calculus and applications. He is the author of more than 55 research papers since 2018 and be part of more than five books published in Taylor Francis and Springer. His research covers mathematical modeling, applied mathematics, numerical analysis, probability and statistics, and fundamental mathematics. He is nominated as a Review Editor of Frontiers in Applied Mathematics and Statistics and Frontiers in Physics. He was a Lead Guest Editor for a special issue published in the Journal of Mathematics Hindawi.

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