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Can Lévy noise induce coherence and stochastic resonances in a birhythmic van der Pol system?

Author

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  • Raoul Mbakob Yonkeu

    (Fundamental Physics Laboratory, University of Bamenda, Faculty of Sciences, Department of Physics)

  • René Yamapi

    (Fundamental Physics Laboratory, Physics of Complex System Group, Department of Physics, Faculty of Science, University of Douala)

  • Giovanni Filatrella

    (INFN Gruppo Collegato Salerno and Department of Sciences and Technologies University of Sannio, Via F. De Sanctis)

  • Jürgen Kurths

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

Abstract

The analysis of a birhythmic modified van der Pol type oscillator driven by periodic excitation and Lévy noise shows the possible occurrence of coherence resonance and stochastic resonance. The frequency of the harmonic excitation in the neighborhood of one of the limit cycles influences the coherence of the dynamics on the time scale of the oscillations. The autocorrelation function, the power spectral density and the signal-to-noise-ratio used in this analysis are shown to be maximized for an appropriate choice of the noise intensity. In particular, a proper adjustment of the Lévy noise intensity enhances the output power spectrum of the system, that is, promotes stochastic resonance. Thus, the resonance, as examined using standard measures, seems to occur also in the presence of nonstandard noise. The initial selection of the attractor seems to have an influence on the coherence, while the skewness parameter of the Lévy noise has not a notable impact on the resonant effect. Graphical abstract

Suggested Citation

  • Raoul Mbakob Yonkeu & René Yamapi & Giovanni Filatrella & Jürgen Kurths, 2020. "Can Lévy noise induce coherence and stochastic resonances in a birhythmic van der Pol system?," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(8), pages 1-14, August.
    • Handle: RePEc:spr:eurphb:v:93:y:2020:i:8:d:10.1140_epjb_e2020-10146-x
    DOI: 10.1140/epjb/e2020-10146-x
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    References listed on IDEAS

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    1. Aleksander Janicki, 1996. "Numerical and Statistical Approximation of Stochastic Differential Equations with Non-Gaussian Measures," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9601, 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. Korneev, Ivan & Zakharova, Anna & Semenov, Vladimir V., 2024. "Lévy noise-induced coherence resonance: Numerical study versus experiment," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    3. Hui, Nirmalendu & Biswas, Debabrata & Bandyopadhyay, Biswabibek & Chakraborty, Meenakshi & Banerjee, Tanmoy, 2024. "Filtering induced explosive death in coupled FitzHugh–Nagumo neurons: Theory and experiment," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    4. 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).

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