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

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.