Effects of a periodic drive and correlated noise on birhythmic van der Pol systems

This paper considers the dynamics of a van der Pol birhythmic oscillator submitted both to colored noise and harmonic excitation. Applying the quasi-harmonic assumption to the corresponding Langevin equation we derive an approximated Fokker-Planck equation, that is compared with the results of computer simulations. We thus derive both the effects of the correlation time and the harmonic excitation on the parameter space where birhythmicity appears. In this region, we find that the multi-limit-cycle van der Pol oscillator reduces to an asymmetric bistable system where the sinusoidal drive intensity plays the role of asymmetric parameter, and noise can lead to stochastic bifurcations, consisting in a qualitative change of the stationary amplitude distribution. Under both influence of noise and harmonic excitation, the dynamics can be well characterized through the concepts of pseudo-potential, that regulates the low noise Arrhenius-like behavior.