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A non-autonomous mega-extreme multistable chaotic system

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  • Ahmadi, Atefeh
  • Parthasarathy, Sriram
  • Natiq, Hayder
  • Jafari, Sajad
  • Franović, Igor
  • Rajagopal, Karthikeyan

Abstract

Megastable and extreme multistable systems comprise two major new branches of multistable systems. So far, they have been studied separately in various chaotic systems. Nevertheless, to the best of our knowledge, no chaotic system has so far been reported that possesses both types of multistability. This paper introduces the first three-dimensional non-autonomous chaotic system that displays megastability and extreme multistability, jointly called mega-extreme multistability. Our model shows extreme multistability for a variation of an initial condition associated with one system variable and megastability concerning another variable. The different types of coexisting attractors are characterized by the corresponding phase portraits and first return maps, as well as by constructing the appropriate bifurcation diagrams, calculating the Lyapunov spectra, the Kaplan-Yorke dimension and the connecting curves, and by determining the corresponding basins of attraction. The system is explicitly shown to be dissipative, with the dissipation being state-dependent. We demonstrate the feasibility and applicability of our model by designing and simulating an appropriate analog circuit.

Suggested Citation

  • Ahmadi, Atefeh & Parthasarathy, Sriram & Natiq, Hayder & Jafari, Sajad & Franović, Igor & Rajagopal, Karthikeyan, 2023. "A non-autonomous mega-extreme multistable chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923006665
    DOI: 10.1016/j.chaos.2023.113765
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    References listed on IDEAS

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    1. Zhang, Sen & Zheng, Jiahao & Wang, Xiaoping & Zeng, Zhigang, 2021. "A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
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    5. Kui Zhang & M. D. Vijayakumar & Sajjad Shaukat Jamal & Hayder Natiq & Karthikeyan Rajagopal & Sajad Jafari & Iqtadar Hussain & Ahmed A. Abd El-Latif, 2021. "A Novel Megastable Oscillator with a Strange Structure of Coexisting Attractors: Design, Analysis, and FPGA Implementation," Complexity, Hindawi, vol. 2021, pages 1-11, August.
    6. Leutcho, Gervais Dolvis & Jafari, Sajad & Hamarash, Ibrahim Ismael & Kengne, Jacques & Tabekoueng Njitacke, Zeric & Hussain, Iqtadar, 2020. "A new megastable nonlinear oscillator with infinite attractors," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    7. Zhang, Yunzhen & Liu, Zhong & Wu, Huagan & Chen, Shengyao & Bao, Bocheng, 2019. "Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 354-363.
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    2. Zhao, Qianhan & Bao, Han & Zhang, Xi & Wu, Huagan & Bao, Bocheng, 2024. "Complexity enhancement and grid basin of attraction in a locally active memristor-based multi-cavity map," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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