Lévy noise-controlled coherence resonance

Abstract

Lévy noise is known to provide for controlling characteristics of noise-induced oscillations when observing various noise-induced phenomena. Based on the study of the FitzHugh-Nagumo system in the excitable regime subject to stochastic impact, we extend this manifold by the investigation of the influence of the Lévy noise properties on the effect of coherence resonance.

In particular, we demonstrate that the Lévy noise can be a constructive or destructive factor providing for enhancement or suppression of noise-induced coherence. We show that the positive or negative role of the Lévy noise impact is dictated by the noise stability index and skewness parameter. The correlation time and the deviation of interspike intervals used in this analysis are shown to be maximized or minimized for an appropriate choice of the noise parameters. Numerical simulations are combined with experiments on an electronic circuit showing an excellent qualitative correspondence and proving thereby the robustness of the observed phenomena.

The numerical and experimental results are in a good correspondence. The presented results clearly indicate that the Lévy noise-induced dynamics is more diverse as compared to a classical, Gaussian stochastic force.

One can find a more detailed description of the obtained results in the recently published paper:
I. Korneev, A. Zakharova, V.V. Semenov, 'Lévy noise-induced coherence resonance: numerical study versus experiment', Chaos, Solitons & Fractals 184, 115037 (2024)

The presented work was supported by the Russian Science Foundation (project No. 23-72-10040).

Speaker

Vladimir Semenov
Saratov State University
Russia

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