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A unique self-driven 5D hyperjerk circuit with hyperbolic sine function: Hyperchaos with three positive exponents, complex transient behavior and coexisting attractors

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  • Vivekanandhan, Gayathri
  • Chedjou, Jean Chamberlain
  • Jacques, Kengne
  • Rajagopal, Karthikeyan

Abstract

We propose a new hyperchaotic hyperjerk-type electronic circuit of remarkable simplicity composed only of simple electronic components. The mathematical model of the circuit, derived by application of Kirchhoff's laws, is presented in the form of a hyperjerk system of order five with a single nonlinearity in the form of hyperbolic sine. The model owns a single unstable equilibrium at the origin. The theoretical analysis yields striking dynamical features including the hyperchaos with three positive Lyapunov exponents, complex transient, coexisting multiple attractors and offset boosting. These properties are illustrated using eigenvalues locus, the plot of bifurcation diagrams, time series, basins of attraction, phase portraits, Poincaré sections as well as the spectrum of Lyapunov exponents. The measurements carried out in the laboratory on an experimental prototype are consistent with the results of the theoretical study. Let us mention that the presence of three positive Lyapunov exponents for an autonomous system of order five with such a simple mathematical model is unprecedented in the literature and deserves to be shared.

Suggested Citation

  • Vivekanandhan, Gayathri & Chedjou, Jean Chamberlain & Jacques, Kengne & Rajagopal, Karthikeyan, 2024. "A unique self-driven 5D hyperjerk circuit with hyperbolic sine function: Hyperchaos with three positive exponents, complex transient behavior and coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008282
    DOI: 10.1016/j.chaos.2024.115276
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    References listed on IDEAS

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    1. Grassi, Giuseppe & Severance, Frank L. & Miller, Damon A., 2009. "Multi-wing hyperchaotic attractors from coupled Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 284-291.
    2. Chlouverakis, Konstantinos E. & Sprott, J.C., 2006. "Chaotic hyperjerk systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 739-746.
    3. Gao, Tiegang & Chen, Zengqiang, 2008. "Image encryption based on a new total shuffling algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 213-220.
    4. 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.
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