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A Novel Megastable Hamiltonian System with Infinite Hyperbolic and Nonhyperbolic Equilibria

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  • Gervais Dolvis Leutcho
  • Theophile Fonzin Fozin
  • Alexis Nguomkam Negou
  • Zeric Tabekoueng Njitacke
  • Viet-Thanh Pham
  • Jacques Kengne
  • Sajad Jafari

Abstract

The dimension of the conservative chaotic systems is an integer and equals the system dimension, which brings about a better ergodic property and thus have potentials in engineering application than the dissipative systems. This paper investigates the phenomenon of megastability in a unique and simple conservative oscillator with infinite of hyperbolic and nonhyperbolic equilibria. Using traditional nonlinear analysis tools, we found that the introduced oscillator possesses an invariable energy and displays either self-excited or hidden dynamics depending on the stability of its equilibria. Besides, the conservative nature of the new system is validated using theoretical measurement. Furthermore, an analog simulator of the oscillator is built and simulated in the PSpice environment to confirm that the previous results were not artifacts.

Suggested Citation

  • Gervais Dolvis Leutcho & Theophile Fonzin Fozin & Alexis Nguomkam Negou & Zeric Tabekoueng Njitacke & Viet-Thanh Pham & Jacques Kengne & Sajad Jafari, 2020. "A Novel Megastable Hamiltonian System with Infinite Hyperbolic and Nonhyperbolic Equilibria," Complexity, Hindawi, vol. 2020, pages 1-12, September.
    • Handle: RePEc:hin:complx:9260823
    DOI: 10.1155/2020/9260823
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    Cited by:

    1. Vijayakumar, M.D. & Natiq, Hayder & Tametang Meli, Maxim Idriss & Leutcho, Gervais Dolvis & Tabekoueng Njitacke, Zeric, 2022. "Hamiltonian energy computation of a novel memristive mega-stable oscillator (MMO) with dissipative, conservative and repelled dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Prasina Alexander & Selçuk Emiroğlu & Sathiyadevi Kanagaraj & Akif Akgul & Karthikeyan Rajagopal, 2023. "Infinite coexisting attractors in an autonomous hyperchaotic megastable oscillator and linear quadratic regulator-based control and synchronization," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(1), pages 1-13, January.

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