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 MFPTs 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₊(s_s1→x_s2) and T_- (x_s2x_s1) are different in the same kind of parameter plane. There exists a peak on each of the curves of lnT_- versus D, as well as the 'resonant activation', while the variation of lnT₊ versus D is monotonic. (3) The influence of the asymmetry coefficient r on T_± is entirely different. The curves of 1nT_- versus r have mono-valleys but the variation of In T₊ versus r is monotonically rising.