MFPT of asymmetric bistable system driven by correlated noises

The effect of every parameter (p, q, r, λ) on the mean first-passage time is investigated in an asymmetric bistable system with correlated multiplicative and additive white noises. The method of the steepest, descent approximation, is used to find the expression of the mean first passage time. The numerical results show that: (1) The strength of correlation of the noise, A, on the mean first-passage time T₊ (x₁→x₂, λ, r) and T_- (x₂→x₁, λ, r) are different in the same kind of parameter plane. The T+ increases and the T_- decreases as A increases. (2) the influence of the multiplicative white noise on T₊ and T_- is entirely different; There exists a peak on the curves of ln T₊ versus p, as well as the resonant peak, while the variation of ln T_- versus p is monotonically decreasing. (3) The effort of the multiplicative noise p on the MFPT is also reflected in other parameters, such as the weakly correlated and strongly correlated noises.