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Coexistence of multi-scroll chaotic attractors for fractional systems with exponential law and non-singular kernel

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  • Mathale, D.
  • Doungmo Goufo, Emile F.
  • Khumalo, M.

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.

Suggested Citation

  • Mathale, D. & Doungmo Goufo, Emile F. & Khumalo, M., 2020. "Coexistence of multi-scroll chaotic attractors for fractional systems with exponential law and non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304197
    DOI: 10.1016/j.chaos.2020.110021
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    References listed on IDEAS

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    Cited by:

    1. Jia, Hongyan & Liu, Jingwen & Li, Wei & Du, Meng, 2023. "A family of new generalized multi-scroll Hamiltonian conservative chaotic flows on invariant hypersurfaces and FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Ahmad, Shabir & Ullah, Aman & Akgül, Ali, 2021. "Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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