关联噪声驱动非对称双稳系统的MFTP

MFPT of Asymmetric Bistable System Driven by Correlated Noises

考虑了由关联噪声驱动的非对称双稳系统的平均首次穿越时间(MFPT)问题,运用最速下降法求得平均首次穿越时间的表达式,并讨论了各个参数(包括p,q,r,λ)对两个方向的平均首次穿越时间的影响。结果表明:1)噪声关联时间λ对平均首次穿越时间T+(x1→x2,λ,r)和T-(x2→x1,λ,r)的影响是不同的,T+随着λ的增加而增加,而T-却随着λ的增加而减小。2)平均首次穿越时间T+(x1→x2,λ,r)和T-(x2→x1,λ,r)都随加性噪声强度q的增加而减小;但乘性噪声P对T+和T-影响却是完全不同的,T-随着P的增加而减小,而T+随着P的增加曲线有一个极大值,即是一个共振峰。3)在不同的噪声关联强度的影响下,T+/T-的曲线随着P的增加呈现不同的发展趋势,λ=0.1时,T+/T-随着P的增加单调减小;而λ=0.7时,T+/T-随着P的增加先增加再减小,曲线出现了极值峰。

The effect of every parameter (p,q,r,λ) on the mean first-passage time is investigated in an asymmetric bistable system with correlated multiplicative and additive white noises. The method of the steepest, descent approximation, is used to find the expression of the mean first passage time. The numerical results show that: (1) The strength of correlation of the noise, λ, on the mean first-passage time T+(x1→x2,λ,r) and T-(x2→x1,λ,r) are different in the same kind of parameter plane. The T+ increases and the T-decreases as λ increases. (2) the influence of the multiplicative white noise on T+ and T-is entirely different; There exists a peak on the curves of ln T+ versus p, as well as the resonant peak, while the variation of ln T-versus p is monotonically decreasing . (3) The effort of the the multiplicative noise p on the MFPT is also reflected in other parameters, such as the weakly correlated and strongly correlated noises.