 Coexistence of multi-scroll chaotic attractors for fractional systems with exponential law and non-singular kernelD. Mathale, Emile F. Doungmo Goufo and M. Khumalo Chaos, Solitons & Fractals, 2020, vol. 139, issue C Abstract: In this paper, we present mathematical analysis and numerical simulation of a three-dimensional autonomous fractional system with coexistence of multi-scroll chaotic attractors. We replaced the classical derivatives of such system with the Caputo-Fabrizio fractional derivative. This derivative combines both the exponential laws and non-singular kernels in its formulation which makes it special and useful. A two-step Adams-Bashforth scheme is derived for the approximation of the fractional derivative with exponential law and non-singular kernel. We then presented both numerical results and graphical results by considering many values of the fractional-order parameter β ∈ (0, ]. We demonstrate that the observed chaotic behavior conduct perseveres as the fractional-order parameter approaches 1. Keywords: Caputo-Fabrizio derivative; Adams-Bashforth method; 3D-dimensional autonomous system; Multi-scroll chaotic attractor; Stability analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304197 DOI: 10.1016/j.chaos.2020.110021 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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