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Hidden Strange Nonchaotic Attractors

Author

Listed:
  • Marius-F. Danca

    (Romanian Romanian Institute of Science and Technology, 400487 Cluj-Napoca, Romania)

  • Nikolay Kuznetsov

    (Department of Applied Cybernetics, Saint-Petersburg State University, Peterhof, 198504 Saint-Petersburg, Russia
    Department of Mathematical Information Technology, University of Jyväskylä, 40014 Jyväskylä, Finland)

Abstract

In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the bifurcation parameter, the hidden attractor is manifestly fractal with aperiodic dynamics, and even the finite-time largest Lyapunov exponent, a measure of trajectory separation with nearby initial conditions, is negative. To verify these characteristics numerically, the finite-time Lyapunov exponents, ‘0-1’ test, power spectra density, and recurrence plot are used. Beside the considered hidden strange nonchaotic attractor, a self-excited chaotic attractor and a quasiperiodic attractor of the Rabinovich–Fabrikant system are comparatively analyzed.

Suggested Citation

  • Marius-F. Danca & Nikolay Kuznetsov, 2021. "Hidden Strange Nonchaotic Attractors," Mathematics, MDPI, vol. 9(6), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:652-:d:519757
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    References listed on IDEAS

    as
    1. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
    2. Lozi, René & Pogonin, Vasiliy A. & Pchelintsev, Alexander N., 2016. "A new accurate numerical method of approximation of chaotic solutions of dynamical model equations with quadratic nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 108-114.
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    Cited by:

    1. Yamauchi, Atsushi & Ito, Koichi & Shibasaki, Shota & Namba, Toshiyuki, 2023. "Continuous irregular dynamics with multiple neutral trajectories permit species coexistence in competitive communities," Theoretical Population Biology, Elsevier, vol. 149(C), pages 39-47.
    2. Ran, Jie & Li, Yu-Qin & Xiong, Yi-Bin, 2022. "On the dynamics of fractional q-deformation chaotic map," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    3. Karthikeyan Rajagopal & Suresh Kumarasamy & Sathiyadevi Kanagaraj & Anitha Karthikeyan, 2022. "Infinitely coexisting chaotic and nonchaotic attractors in a RLC shunted Josephson Junction with an AC bias current," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(9), pages 1-9, September.
    4. Asir, M. Paul & Thamilmaran, K. & Prasad, Awadhesh & Feudel, Ulrike & Kuznetsov, N.V. & Shrimali, Manish Dev, 2023. "Hidden strange nonchaotic dynamics in a non-autonomous model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    5. Ahmed A. Abd El-Latif & Janarthanan Ramadoss & Bassem Abd-El-Atty & Hany S. Khalifa & Fahimeh Nazarimehr, 2022. "A Novel Chaos-Based Cryptography Algorithm and Its Performance Analysis," Mathematics, MDPI, vol. 10(14), pages 1-22, July.

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