色噪声驱动的非对称双稳系统的平均首次穿越时间  

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

作　　者：张娜敏[1] 徐伟[1] 王朝庆[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《物理学报》2007年第9期5083-5087,共5页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10472091;10332030)资助的课题.~~

摘　　要：研究了由关联乘性色噪声及加性白噪声驱动的非对称双稳系统中势阱的非对称性及噪声对系统两个方向平均首次穿越时间的影响.首先利用一致有色噪声近似推导了系统的稳态概率密度的表达式,根据最速下降法推导了平均首次穿越时间的表达式.数值结果表明:势阱的非对称性对两个方向的平均首次穿越时间的影响是不同的;由于噪声的关联性,即使对于关联乘性色噪声及加性白噪声驱动的对称双稳系统,两个方向的平均首次穿越时间也不再相等;在lnT+-r和lnT--r曲线上都存在极小值,不同的是在lnT+-r曲线上极小值的位置随λ增大逐渐右移,而在lnT--r曲线上极小值的位置随λ增大逐渐左移.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 s2 →x s1 ,r）. The curves of lnT± versus r in both cases have mono-valleys but the mono-valleys move to the opposite directions with increasing correlation intensity λ.

关 键 词：平均首次穿越时间 非对称双稳系统 乘性色噪声 加性白噪声 

分 类 号：O324[理学—一般力学与力学基础]