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Dynamics of two coupled van der Pol–Mathieu oscillators

Author

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  • Ramazanov, Ibadulla R.
  • Korneev, Ivan A.
  • Vadivasova, Tatiana E.
  • Slepnev, Andrei V.

Abstract

The interaction of two van der Pol–Mathieu oscillators, the simplest models of self-oscillatory systems with parametric excitation, is studied. The dynamics of an individual oscillator is determined either by its self-oscillatory or parametric component, therefore, all possible combinations are considered: both oscillators in a self-oscillatory regime; both oscillators in parametric regime; one oscillator in self-oscillatory regime, another one in parametric regime. To determine the nature of the system dynamics, both complete equations and averaged equations for amplitudes and phases are used, Lyapunov exponents, sections of phase trajectories, and oscillation power spectra are calculated. The behavior of the system under study is compared with the classical case of the interaction of two dissipatively coupled van der Pol oscillators.

Suggested Citation

  • Ramazanov, Ibadulla R. & Korneev, Ivan A. & Vadivasova, Tatiana E. & Slepnev, Andrei V., 2024. "Dynamics of two coupled van der Pol–Mathieu oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003916
    DOI: 10.1016/j.chaos.2024.114839
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    References listed on IDEAS

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    1. Mbakob Yonkeu, R. & David, Afungchui, 2022. "Coherence and stochastic resonance in the fractional-birhythmic self-sustained system subjected to fractional time-delay feedback and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    2. René Yamapi & Raoul Mbakob Yonkeu & Giovanni Filatrella & Jürgen Kurths, 2019. "Lévy noise induced transitions and enhanced stability in a birhythmic van der Pol system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(7), pages 1-13, July.
    3. Yonkeu, R. Mbakob, 2023. "Stochastic bifurcations induced by Lévy noise in a fractional trirhythmic van der Pol system," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
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