非对称双稳系统中平均首次穿越时间的研究

研究了由乘性白噪声和加性白噪声驱动的非对称双稳系统中，势阱的非对称性对两个不同方 向的平均首次穿越时间的影响.发现在非对称双稳系统中，两个不同方向的平均首次穿越时 间是与初始状态有关.此外，对一维非对称达芬模型的平均首次穿越时间进行了研究.数值结 果表明：(1) 非对称双稳系统的平均首次穿越时间对初始状态有“记忆性”；(2) 噪声强度 对两个不同方向的平均首次穿越时间T₊（x_s1→x_s2)和 T_-(x_s2→x_s1)的影响是不同的：lnT_--Ｄ 曲线上存在峰值，出 现了“共振”现象，而lnＴ₊-Ｄ曲线是单调的；(3) 势阱的非对称性r对T ₊（x_s1→x_s2)和T_-(x_s2→x_s1 )的影响是不 同的：lnＴ_--r曲线上存在极小值，出现了“抑制”现象，而lnＴ₊ -r曲线是单调的. 关键词： 平均首次穿越时间 非对称双稳系统 乘性噪声 加性噪声

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 b istable system driven by multiplicative noise and additive noise. We find that t he MFPTs in two opposite directions are no longer symmetric in an asymmetric bis table system. Furthermore, we calculate the MFPTs of an asymmetric Duffing model . Numerical results show that: (1) The MFPTs depend on the initial states in th e asymmetric bistable system, namely, T₊(x_s1→x_{s2) is not equal to T-(xs2→xs1). (2) The effec ts of noise intensity on the MFPTs T+(xs1→xs2) and T-( xs2→xs1) are different in the same kind of parameter plan e. There exists a peak on each of the curves of lnＴ- versus Ｄ,as we ll as the “resonant activation”, while the variation of lnＴ+ ver sus Ｄ is monotonic. (3) The influence of the asymmetry coefficient r on Ｔ± is entirely different. The curves of lnT- versus r have mon o-valleys but the variation of lnＴ+ versus r is monotonically risi ng.}