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Lévy noise induced transitions and enhanced stability in a birhythmic van der Pol system

Author

Listed:
  • René Yamapi

    (Fundamental Physics Laboratory, Physics of Complex System Group, Department of Physics, Faculty of Science, University of Douala
    Potsdam Institute for Climate Impact Research (PIK))

  • Raoul Mbakob Yonkeu

    (Laboratory of Mechanics and Materials, Department of Physics, Faculty of Science, University of Yaoundé I)

  • Giovanni Filatrella

    (University of Sannio)

  • Jürgen Kurths

    (Potsdam Institute for Climate Impact Research (PIK)
    Humboldt University)

Abstract

This work describes the effects of Lévy noise on a birhythmic van der Pol like oscillator. The two periodic attractors are characterized by different periods, and the stability in the presence of Gaussian noise can be described by an effective, or quasi-potential. Numerical simulations demonstrate that in the presence of Lévy noise the induced escapes from an attractor to another are similar to the escapes between stable points in an ordinary potential. Assuming that the attractors are almost separated by a barrier of a quasi (or pseudo) potential, the theory for Lévy noise escapes captures the qualitative features of the escapes across the quasi-potential. The differences to the Gaussian case are more pronounced for large values of the Lévy index. We found that for the symmetric quasi-potential, the relative stability of the two attractors are similar, while in the asymmetric case the properties of the two attractors differ for increasing a. The global stability is also characterized by means of the residence times, that give indications for future theoretical analysis. Graphical abstract

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurphb:v:92:y:2019:i:7:d:10.1140_epjb_e2019-100029-x
    DOI: 10.1140/epjb/e2019-100029-x
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    References listed on IDEAS

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    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401, December.
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    Cited by:

    1. 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).
    2. 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).
    3. Slepukhina, Evdokia & Bashkirtseva, Irina & Ryashko, Lev, 2020. "Stochastic spiking-bursting transitions in a neural birhythmic 3D model with the Lukyanov-Shilnikov bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

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