The mean first-passage time for an asymmetric bistable system driven by multiplicative colored and additive white noise with a correlated noise

We investigated the effects of asymmetry of the potential and noises on the mean first-passage time (MFPT) in two opposite directions in an asymmetric bistable system subjected to multiplicative colored and additive white noise with a correlated noise. The expression of the stationary probability distribution is obtained by means of an extended unified colored-noise approximation and the expressions of the MFPTs are derived through the steepest-descent approach. Numerical results show that the influence of the asymmetry coefficient r on T _∓ is different and because of the correlated noise, even for r = 0, T ₊ (x_s1→x_s2, r) is not equal to T_- (x_s1→x_s2, r). The curves of InT_∓ versus r in both cases have mono-valleys but the mono-valleys move to the opposite directions with increasing correlation intensity λ.