Multistability route in a PWL multi-scroll system through fractional-order derivatives

J.L. Echenausía-Monroy, H.E. Gilardi-Velázquez, Ning Wang, R. Jaimes-Reátegui, J.H. García-López and G. Huerta-Cuellar

Chaos, Solitons & Fractals, 2022, vol. 161, issue C

Abstract: Recently, it was discovered that the use of fractional derivatives induces the occurrence of multistable states in PWL systems with multiple scrolls. In this paper, we show the emergence of multistable states in a PWL system and study the route of the system to transition from monostable to multistable behavior by reducing the order of the fractional derivative. Using bifurcation diagrams that describe the evolution of the attractor as a consequence of the change in derivative order and basins of attraction, we show that the system has a path to multistability that reveals the mechanism for the occurrence of this behavior. The resulting dynamics shows the coexistence of up to n + 2 attractors, where n is the number of scrolls generated by the integer-order system, which has been confirmed for two different n-multi-scrolls systems. Moreover, the existence and uniqueness of the dynamics is proved by Poincaré sections, which show that the behaviors exist, and coexist, and are not a section of the same solution.

Keywords: Fractional-order system; Nonlinear dynamics; Chaotic system; Multistability; PWL system; Bifurcation (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005653

DOI: 10.1016/j.chaos.2022.112355

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