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Inducing multistability in discrete chaotic systems using numerical integration with variable symmetry

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  • Ostrovskii, Valerii Yu.
  • Rybin, Vyacheslav G.
  • Karimov, Artur I.
  • Butusov, Denis N.

Abstract

Multistability is an inherent property of many nonlinear dynamical systems. However, finding exact conditions where a certain nonlinear system is multistable, is a complex problem. In this study, we propose a novel approach for inducing multistability in a discrete system by applying the numerical integration method with variable symmetry to a continuous monostable system and finding a range of the symmetry coefficients for which multiple attractors coexist in its discrete model. We consider the well-known Chen system as an example, showing that multistability can be induced by discretization with variable symmetry. A special two-stage algorithm is proposed for a fast search for hidden attractors. Using the proposed algorithm, we found several multistable versions of the discrete Chen system and investigated their attractors and basins of attraction. By applying numerical backward error analysis, we discovered a generalized continuous Chen system with additional terms which were not present in the original system and have shown its approximate equivalence to the obtained discrete system. The results of this study can be used for inducing artificial multistability in a wide range of chaotic systems with possible applications in chaotic cryptography, communication, and chaos-based sensing.

Suggested Citation

  • Ostrovskii, Valerii Yu. & Rybin, Vyacheslav G. & Karimov, Artur I. & Butusov, Denis N., 2022. "Inducing multistability in discrete chaotic systems using numerical integration with variable symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009730
    DOI: 10.1016/j.chaos.2022.112794
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    References listed on IDEAS

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    1. Bao, B.C. & Bao, H. & Wang, N. & Chen, M. & Xu, Q., 2017. "Hidden extreme multistability in memristive hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 102-111.
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    4. Tutueva, Aleksandra V. & Moysis, Lazaros & Rybin, Vyacheslav G. & Kopets, Ekaterina E. & Volos, Christos & Butusov, Denis N., 2022. "Fast synchronization of symmetric Hénon maps using adaptive symmetry control," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    5. Tutueva, Aleksandra V. & Nepomuceno, Erivelton G. & Karimov, Artur I. & Andreev, Valery S. & Butusov, Denis N., 2020. "Adaptive chaotic maps and their application to pseudo-random numbers generation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    6. Artur Karimov & Erivelton G. Nepomuceno & Aleksandra Tutueva & Denis Butusov, 2020. "Algebraic Method for the Reconstruction of Partially Observed Nonlinear Systems Using Differential and Integral Embedding," Mathematics, MDPI, vol. 8(2), pages 1-22, February.
    7. Bao, H. & Gu, Y. & Xu, Q. & Zhang, X. & Bao, B., 2022. "Parallel bi-memristor hyperchaotic map with extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    8. Frank Hellmann & Paul Schultz & Patrycja Jaros & Roman Levchenko & Tomasz Kapitaniak & Jürgen Kurths & Yuri Maistrenko, 2020. "Network-induced multistability through lossy coupling and exotic solitary states," Nature Communications, Nature, vol. 11(1), pages 1-9, December.
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    Cited by:

    1. N. C. Pati, 2023. "Bifurcations and multistability in a physically extended Lorenz system for rotating convection," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-15, August.
    2. Ivan Babkin & Vyacheslav Rybin & Valery Andreev & Timur Karimov & Denis Butusov, 2024. "Coherent Chaotic Communication Using Generalized Runge–Kutta Method," Mathematics, MDPI, vol. 12(7), pages 1-21, March.

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