Effects of noise correlation on the coherence of a forced van der Pol type birhythmic system

Abstract We investigate the effects of noise correlation on the coherence of a forced van der Pol type birhythmic system. The coherence of the dynamics on the time scale of intrawell oscillations, as measured by the signal-to-noise- ratio, is shown to be maximized for an appropriate choice of the noise intensity and of the noise correlation time . Other measures, related to the autocorrelation function and applicable on the longer time scale of interwell oscillations do not exhibit such nonlinear behavior. When occurs, the coherence appears similar to noise induced stochastic resonance in ordinary bistable potential systems, while the investigated birhythmic system only posses a nonequilibrium or quasi-potential associated to the orbits. Thus, it is demonstrated that correlated noise, even if the attractors are not fix points but orbits, can give rise to stochastic resonance.