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Dynamical analysis of a novel autonomous 4-D hyperjerk circuit with hyperbolic sine nonlinearity: Chaos, antimonotonicity and a plethora of coexisting attractors

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  • Leutcho, G.D.
  • Kengne, J.
  • Kengne, L. Kamdjeu

Abstract

In this paper, a novel fourth-order autonomous hyperjerk circuit is proposed and the corresponding dynamics is systematically analyzed. Two anti-parallel semiconductor diodes form the nonlinear component necessary for chaotic oscillations. The mathematical model of the novel circuit consists of a fourth-order (“elegant”) autonomous hyperjerk system with (a single) hyperbolic sine nonlinearity. The fundamental dynamic properties of the model are investigated including fixed points and stability, phase portraits, bifurcation diagrams, and Lyapunov exponent plots. Period-doubling bifurcation, periodic windows, coexisting bifurcations, symmetry recovering crises, and antimonotonicity (i.e. concurrent creation and annihilation of periodic orbit) are reported when monitoring the systems parameters. One of the main findings in this work is the presence of various windows in the parameter space in which the novel 4D-hyperjerk system develops the interesting property of multiple coexisting attractors (e.g. coexistence of two, three, four, five, six, seven height or nine disconnected periodic and chaotic attractors). To the best of the authors’ knowledge, this striking phenomenon is unique and has not yet been reported previously in a hyperjerk circuit, and thus represents a significant contribution to the understanding of the behavior of nonlinear dynamical systems in general. Laboratory experiments of the oscillator are carried out to verify the theoretical analysis.

Suggested Citation

  • Leutcho, G.D. & Kengne, J. & Kengne, L. Kamdjeu, 2018. "Dynamical analysis of a novel autonomous 4-D hyperjerk circuit with hyperbolic sine nonlinearity: Chaos, antimonotonicity and a plethora of coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 67-87.
    • Handle: RePEc:eee:chsofr:v:107:y:2018:i:c:p:67-87
    DOI: 10.1016/j.chaos.2017.12.008
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    1. Linz, Stefan J., 2008. "On hyperjerky systems," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 741-747.
    2. Manimehan, I. & Philominathan, P., 2012. "Composite dynamical behaviors in a simple series–parallel LC circuit," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1501-1509.
    3. Hanias, M.P. & Giannaris, G. & Spyridakis, A. & Rigas, A., 2006. "Time series analysis in chaotic diode resonator circuit," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 569-573.
    4. Chlouverakis, Konstantinos E. & Sprott, J.C., 2006. "Chaotic hyperjerk systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 739-746.
    5. Munmuangsaen, Buncha & Srisuchinwong, Banlue, 2011. "Elementary chaotic snap flows," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 995-1003.
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    3. Leutcho, Gervais Dolvis & Kengne, Jacques, 2018. "A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 275-293.
    4. 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).
    5. Kamdjeu Kengne, Léandre & Mboupda Pone, Justin Roger & Fotsin, Hilaire Bertrand, 2021. "On the dynamics of chaotic circuits based on memristive diode-bridge with variable symmetry: A case study," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    6. Tametang Meli, Maxim Idriss & Yemélé, David & Leutcho, Gervais Dolvis, 2021. "Dynamical analysis of series hybrid electric vehicle powertrain with torsional vibration: Antimonotonicity and coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    7. Zhang, Xu & Min, Fuhong & Dou, Yiping & Xu, Yeyin, 2023. "Bifurcation analysis of a modified FitzHugh-Nagumo neuron with electric field," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    8. Xianyang Xie & Shiping Wen & Yuming Feng & Babatunde Oluwaseun Onasanya, 2022. "Three-Stage-Impulse Control of Memristor-Based Chen Hyper-Chaotic System," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    9. Signing, V.R. Folifack & Kengne, J. & Kana, L.K., 2018. "Dynamic analysis and multistability of a novel four-wing chaotic system with smooth piecewise quadratic nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 263-274.
    10. Cheng, Guanghui & Gui, Rong, 2022. "Bistable chaotic family and its chaotic mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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