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Constructing and analyzing of a unique three-dimensional chaotic autonomous system exhibiting three families of hidden attractors

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  • Kingni, Sifeu Takougang
  • Jafari, Sajad
  • Pham, Viet-Thanh
  • Woafo, Paul

Abstract

A three-dimensional chaotic autonomous system is proposed in this paper. This system has a unique property: it can belong to three different families of chaotic systems with hidden attractors: (a) systems with a line of equilibria, (b) systems with only stable equilibria, and (c) systems with no equilibria. Dynamics of this system are investigated through eigenvalue structures, phase portraits, basin of attraction, bifurcation diagram and Lyapunov exponents. The physical existence of the chaotic behavior found in the proposed system is verified by using OrCAD-PSpice software. A good qualitative agreement is shown between the simulations and the PSpice results.

Suggested Citation

  • Kingni, Sifeu Takougang & Jafari, Sajad & Pham, Viet-Thanh & Woafo, Paul, 2017. "Constructing and analyzing of a unique three-dimensional chaotic autonomous system exhibiting three families of hidden attractors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 172-182.
    • Handle: RePEc:eee:matcom:v:132:y:2017:i:c:p:172-182
    DOI: 10.1016/j.matcom.2016.06.010
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    References listed on IDEAS

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    1. Kingni, S.T. & Nana, B. & Mbouna Ngueuteu, G.S. & Woafo, P. & Danckaert, J., 2015. "Bursting oscillations in a 3D system with asymmetrically distributed equilibria: Mechanism, electronic implementation and fractional derivation effect," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 29-40.
    2. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
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    Cited by:

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