The mean first-passage time for an asymmetric bistable system driven by multiplicative and additive noise

In this paper, the effects of asymmetry of the potential on the mean first-passage times (MFPTs) in two opposite directions are investigated in an asymmetric bistable system driven by multiplicative noise and additive noise. We find that the MFPTs in two opposite directions are no longer symmetric in an asymmetric bistable system. Furthermore, we calculate the MFPFs of an asymmetric Duffing model. Numerical results show that: (1) The MFPTs depend on the initial states in the asymmetric bistable system, namely, T+ (x(s1) -> x(s2)) is not equal to T-_(x(s2) -> x(s1)). (2) The effects of noise intensity on the MFPTs T+ (x(s1) -> x(s2)) and T- (x(s2) -> x(s1)) are different in the same kind of parameter plane. There exists a peak on each of the curves of InT- versus D, as well as the "resonant activation", while the variation of InT+ versus D is monotonic. (3) The influence of the asymmetry coefficient r on T+/- is entirely different. The curves of InT- versus r have mono-valleys but the variation of InT+ versus r is monotonically rising.