非高斯噪声激励下分段非线性系统的平均首次穿越时间  

Mean First-passage Time of a Piecewise Nonlinear Model Driven by Multiplicative Non-Gaussian Noise and Additive White Noise

作　　者：郭永峰[1] 申雅君[1] GUO Yong-feng;SHEN Ya-jun(School of Science, Tianjin Polytechnic University, Tianjin 300387)

机构地区：[1]天津工业大学理学院,天津300387

出　　处：《工程数学学报》2016年第4期339-348,共10页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11102132);天津市应用基础与前沿技术研究计划项目(15JCQNJC04000)~~

摘　　要：噪声诱导的逃逸问题出现在众多研究领域,平均首次穿越时间作为用来表征粒子逃逸现象的重要特征量,现已被广泛应用于电子器件的开关时间及双稳器件的寿命等问题的研究之中.本文研究了由乘性非高斯噪声和加性高斯白噪声共同驱动下分段非线性系统的平均首次穿越时间问题.运用路径积分法、统一色噪声近似和最速下降法,得到了系统平均首次穿越时间的表达式.通过数值计算发现,在非高斯噪声偏离参数、噪声关联时间和互关联强度的作用下,非高斯噪声强度的增加会导致平均首次穿越时间曲线出现单峰结构,而加性噪声强度的增加会导致平均首次穿越时间的单调减小,这表明在该模型中非高斯噪声和高斯噪声对平均首次穿越时间的影响是不同的.此外还进一步讨论了非高斯噪声偏离参数、噪声关联时间和噪声互关联强度对平均首次穿越时间的影响.The noise-induced escape problem in stochastic systems has appeared in many fields. In most of the existing theoretical studies on this topic, the mean first-passage time (MFPT) is introduced to quantify the characteristic quantity of escape process. It has been applied to many problems, such as the switching time problem of electronic devices and the life of bistable devices problem. In this paper, we study the MFPT in a piecewise nonlinear model driven by correlated noises for the cases of multiplicative non-Gaussian noise and an additive Gaussian white noise. By using the path integral method, the unified colored noise approximation and the steepest-descent approximation method, the expression of the MFPT is derived. Numerical computation results show that, under the effect of non-Gaussian noise deviating from the Gaussian distribution, correlation time of the non-Gaussian noise and crosscorrelation strength, increasing the intensity of non-Gaussian noise leads to the appearance of a one-peak structure in the MFPT. However, the MFPT of the system decreases with the increase of the additive white noise intensity. This shows that MFPT corresponding to the non-Gaussian noise and Gaussian white noise exhibits very different behavior. In addition, we also discuss the effect of the degree of non-Gaussian noise deviating from the Gaussian distribution, correlation time of the non-Gaussian noise and cross-correlation strength on MFPT.

关 键 词：非高斯噪声 分段非线性系统 平均首次穿越时间 FOKKER-PLANCK方程 

分 类 号：O211[理学—概率论与数理统计]