Can L\`evy noise induce coherence and stochastic resonances in a birhythmic van der Pol system?

TL;DR

This paper investigates how L extquoteright evy noise can induce coherence and stochastic resonances in a birhythmic van der Pol oscillator, revealing that noise intensity and excitation frequency significantly affect resonance phenomena.

Contribution

It demonstrates that nonstandard L extquoteright evy noise can promote coherence and stochastic resonance in a birhythmic van der Pol system, extending understanding of noise-induced effects.

Findings

Optimal noise intensity maximizes autocorrelation and power spectral density.

L extquoteright evy noise enhances stochastic resonance in the system.

Resonance robustness is confirmed even with non-Gaussian noise.

Abstract

The analysis of a birhythmic modified van der Pol type oscillator driven by periodic excitation and L\`evy 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 intrawell 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. A proper adjustment of the L\`evy noise intensity enhances the output power spectrum of the system, that is, promotes stochastic resonance. Thus, the robustness of the resonance, that seems to occur also in the presence of nonstandard noise, is examined using standard measures. The initial selection of the attractor seems to have an influence on the coherence, while the skewness parameter of the L\`evy noise has not a notable impact on the resonant effect.