Stochastic Bifurcations induced by correlated Noise in a Birhythmic van der Pol System

TL;DR

This paper analyzes how exponentially correlated noise influences the dynamics and bifurcations of birhythmic van der Pol oscillators, revealing that noise parameters can induce stochastic bifurcations.

Contribution

It introduces an analytical approach to study stochastic bifurcations in birhythmic oscillators under correlated noise, extending understanding of noise-induced phenomena.

Findings

Noise correlation time affects oscillator dynamics

Bifurcation parameters include noise intensity and correlation time

Analytical results agree with numerical simulations

Abstract

We investigate the effects of exponentially correlated noise on birhythmic van der Pol type oscillators. The analytical results are obtained applying the quasi-harmonic assumption to the Langevin equation to derive an approximated Fokker-Planck equation. This approach allows to analytically derive the probability distributions as well as the activation energies associated to switching between coexisting attractors. The stationary probability density function of the van der Pol oscillator reveals the influence of the correlation time on the dynamics. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that noise intensity and correlation time can be treated as bifurcation parameters. Comparing the analytical and numerical results, we find good agreement both when the frequencies of the attractors are about equal or when they are markedly different.