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A novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability

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  • Mezatio, Brice Anicet
  • Motchongom, Marceline Tingue
  • Wafo Tekam, Blaise Raoul
  • Kengne, Romanic
  • Tchitnga, Robert
  • Fomethe, Anaclet

Abstract

This paper presents a 6D autonomous system, obtained by introducing a flux-controlled memristor model into an existing 5D hyperchaotic autonomous system. The dynamics of the novel system are investigated in terms of equilibrium points, bifurcation diagrams, Lyapunov exponent spectra, phase portraits, time series and attraction basins. Moreover, its circuit implementation is also proposed. The system is hyperchaotic under a line or a plan of equilibria. Other attractive dynamics observed are: hidden extreme multistability, transient chaos, bursting and offset boosting phenomenon. Interestingly, for a particular set of parameters, an unusual metastability showing transition from chaotic to periodic bursting dynamics is found. Dynamical systems capable of producing the above complexity are not common in the literature; thus, this novel memristive 6D hyperchaotic autonomous system deserves particular attention. PSpice based simulations are in good agreement with numerical computations. To the best of our knowledge, this system is the first with higher order presenting all those phenomena.

Suggested Citation

  • Mezatio, Brice Anicet & Motchongom, Marceline Tingue & Wafo Tekam, Blaise Raoul & Kengne, Romanic & Tchitnga, Robert & Fomethe, Anaclet, 2019. "A novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 100-115.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:100-115
    DOI: 10.1016/j.chaos.2019.01.015
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    7. 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).
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    9. Yan, Shaohui & Wang, Ertong & Gu, Binxian & Wang, Qiyu & Ren, Yu & Wang, Jianjian, 2022. "Analysis and finite-time synchronization of a novel double-wing chaotic system with transient chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    10. Li, Kexin & Bao, Bocheng & Ma, Jun & Chen, Mo & Bao, Han, 2022. "Synchronization transitions in a discrete memristor-coupled bi-neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    11. Jiang Wang & Yang Gu & Kang Rong & Quan Xu & Xi Zhang, 2022. "Memristor-Based Lozi Map with Hidden Hyperchaos," Mathematics, MDPI, vol. 10(19), pages 1-12, September.
    12. Lin, Hairong & Wang, Chunhua & Du, Sichun & Yao, Wei & Sun, Yichuang, 2023. "A family of memristive multibutterfly chaotic systems with multidirectional initial-based offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    13. Zhang, Shaohua & Zhang, Hongli & Wang, Cong, 2023. "Memristor initial-boosted extreme multistability in the novel dual-memristor hyperchaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    14. Njitacke, Zeric Tabekoueng & Doubla, Isaac Sami & Mabekou, Sandrine & Kengne, Jacques, 2020. "Hidden electrical activity of two neurons connected with an asymmetric electric coupling subject to electromagnetic induction: Coexistence of patterns and its analog implementation," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    15. Leng, Xiangxin & Gu, Shuangquan & Peng, Qiqi & Du, Baoxiang, 2021. "Study on a four-dimensional fractional-order system with dissipative and conservative properties," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    16. Chen, Mo & Wang, Chao & Bao, Han & Ren, Xue & Bao, Bocheng & Xu, Quan, 2020. "Reconstitution for interpreting hidden dynamics with stable equilibrium point," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    17. Hairong Lin & Chunhua Wang & Fei Yu & Jingru Sun & Sichun Du & Zekun Deng & Quanli Deng, 2023. "A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    18. Gritli, Hassène, 2019. "Poincaré maps design for the stabilization of limit cycles in non-autonomous nonlinear systems via time-piecewise-constant feedback controllers with application to the chaotic Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 127-145.
    19. Chen, Mo & Ren, Xue & Wu, Huagan & Xu, Quan & Bao, Bocheng, 2020. "Interpreting initial offset boosting via reconstitution in integral domain," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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