有噪及无噪的时滞细胞神经网络稳定性分析  

Stability Analysis of Delayed Cellular Neural Networks With and Without Noise Perturbation

作　　者：张雪娟[1] 王冠香[2] 刘华[3] 

机构地区：[1]浙江绍兴文理学院数学系,浙江绍兴312000 [2]北京大学数学科学学院,北京100871 [3]北京大学光华管理学院,北京100871

出　　处：《应用数学和力学》2008年第11期1293-1302,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10771155);全国优秀博士学位论文作者专项基金资助项目

摘　　要：分析了一类时滞细胞神经网络(DCNN)系统在无噪声和有噪声干扰情况下的稳定性.首先针对确定性系统给出了一种简单且容易验证的全局指数稳定性条件,然后讨论了噪声干扰下系统的稳定性.当DCNN被外部噪声扰动时,系统是全局稳定的.重要的是,当系统被内在噪声扰动时,只要噪声总强度控制在一定范围内,系统是全局指数稳定的.鉴于随机共振现象在越来越多的非线性生物系统中被发现,这种稳定性具有重要意义.The stability of a class of delayed cellular neural networks （DCNN） either without or with noise perturbation are studied. After presenling a simple and easily checkable condition for global exponential stability of the deterministic system, the situations with noise perturbation were further investigate. When the DCNN is perturbed with an external noise, the system is globally stable. The important fact is that, when the system is perturbed with an internal noise, it＇ s globally exponentially stable ff only the total strength of the noise is within a certain bound. This fact is significant as stochastic resonance phenomena have been found exist in many nonlinear systems.

关 键 词：时滞细胞神经网络 全局指数稳定性 外部\内部噪声 

分 类 号：O175[理学—数学] O221[理学—基础数学]