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On the Poisson Stability to Study a Fourth-Order Dynamical System with Quadratic Nonlinearities

Author

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  • Alexander N. Pchelintsev

    (Department of Higher Mathematics, Tambov State Technical University, ul. Sovetskaya 106, 392000 Tambov, Russia)

Abstract

This article discusses the search procedure for Poincaré recurrences to classify solutions on an attractor of a fourth-order nonlinear dynamical system, using a previously developed high-precision numerical method. For the resulting limiting solution, the Lyapunov exponents are calculated, using the modified Benettin’s algorithm to study the stability of the found regime and confirm the type of attractor.

Suggested Citation

  • Alexander N. Pchelintsev, 2021. "On the Poisson Stability to Study a Fourth-Order Dynamical System with Quadratic Nonlinearities," Mathematics, MDPI, vol. 9(17), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2057-:d:622293
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    References listed on IDEAS

    as
    1. 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.
    2. V. Anishchenko & M. Khairulin & G. Strelkova & J. Kurths, 2011. "Statistical characteristics of the Poincaré return times for a one-dimensional nonhyperbolic map," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 82(3), pages 219-225, August.
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    Cited by:

    1. Alexander N. Pchelintsev, 2022. "On a High-Precision Method for Studying Attractors of Dynamical Systems and Systems of Explosive Type," Mathematics, MDPI, vol. 10(8), pages 1-12, April.
    2. António M. Lopes & J. A. Tenreiro Machado, 2022. "Nonlinear Dynamics," Mathematics, MDPI, vol. 10(15), pages 1-3, July.

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