非关联噪声驱动的单稳系统的平均首次穿越时间

The mean first-passage time in a mono-stable system driven by uncorrelated noises

基于非对称双稳系统的理论研究了偏单稳系统的平均首次穿越时间问题,并基于势函数分析了参数对平均首次穿越时间的影响.得出结论:1)当偏稳系数为零时,随着加性噪声强度和参数a的增加,两个方向的平均首次穿越时间相等且均单调减小,2)随着偏稳系数b的增加,势阱的对称性被破坏,粒子由xs1跃迁到xs2的时间线性地减小,而粒子由xs2跃迁到xs1的时间线性地增加.3)随着乘性噪声强度和加性噪声强度比率R的增加,两个方向平均首次穿越时间均单调增加.

In this paper,the mean first-passage time （MFPT） in a biased mono-stable system is investigated on the basis of the theory used in an asymmetric bistable system. The effects of parameters on MFPT are also analyzed based on the generalized potential function. The results show that,first,with parameter a and additive noise intensity Q increasing,the MFPTs in two directions both decrease on condition that bias parameter b is equal to zero; second,the time in which the particle jumps from xs1 to xs2 linearly decreases while the time in which the particle jumps from xs2 to xs1 linearly increases, owing to the fact that the symmetry of potential well is broken by the increase of bias parameter b; finally,the MFPTs in two directions monotonically increase as the ratio of multiplicative noise intensity to the additive noise intensity increases.