Stochastic bifurcations induced by correlated noise in a birhythmic van der Pol system

• We investigate correlated noise in a birhythmic van der Pol type oscillator.
• The noise intensity and correlation can determine the number of stable orbits.
• The analysis based on stochastic averaging is confirmed by numerical simulations.
• The analysis is accurate even in presence of two stable frequencies.

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.