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On chaotic models with hidden attractors in fractional calculus above power law

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  • Doungmo Goufo, Emile Franc

Abstract

Researchers around the world are still wondering about the real origin and causes of hidden oscillating regimes and hidden attractors exhibited by some non-linear complex models. Such models are characterized by a dynamic with a basin of attraction that does not contain neighborhoods of equilibrium points. In this paper, we show that hidden oscillating regimes and hidden attractors can also exist in systems resulting from a combination with fractional differentiation. We apply a fractional derivative with Mittag–Leffler Kernel to a dynamical system with an exponential non-linear term and analyzed the resulting model both analytically and numerically. The combined model, which has no equilibrium points is however shown to display complex oscillating trajectories that culminate in chaos. Numerical simulations show some bifurcation dynamics with respect to the derivative order β and prove that the observed chaotic behavior persists as β varies. These observations made here allow us to say that the fractional model under study belongs to the category of systems with hidden oscillations.

Suggested Citation

  • Doungmo Goufo, Emile Franc, 2019. "On chaotic models with hidden attractors in fractional calculus above power law," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 24-30.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:24-30
    DOI: 10.1016/j.chaos.2019.06.025
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    References listed on IDEAS

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    1. Zhen Wang, 2013. "A Numerical Method for Delayed Fractional-Order Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, May.
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    Cited by:

    1. Fendzi-Donfack, Emmanuel & Kamkou Temgoua, Gildas William & Djoufack, Zacharie Isidore & Kenfack-Jiotsa, Aurélien & Nguenang, Jean Pierre & Nana, Laurent, 2022. "Exotical solitons for an intrinsic fractional circuit using the sine-cosine method," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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