Stochastic resonance across bifurcations in an asymmetric system

Abstract

Stochastic resonance across bifurcations in a non-smooth system with an asymmetric potential under colored noise excitations is investigated. The asymmetry of the potential leads to complex bifurcations in the system. When the system moves across different bifurcation regions, the adiabatic elimination theory and linear response theory are used to analyze the mean first passage time and stochastic resonance. It is shown that multistability of the system reduces the mean first passage time between the two steady states. The mean first passage time in two opposite directions is different caused by the asymmetry of the system and exhibits a suppression platform as the bifurcation parameter varies. For the stochastic resonance, the multistability of the system increases two response amplitudes, but the asymmetry of the potential decreases one response amplitude, while retaining the other response amplitude. Moreover, in two bifurcation regions, the effects of the correlation time of the colored noise on the response amplitudes are different since the system undergoes a saddle–node bifurcation and a pitchfork bifurcation, respectively.