随机时滞反应扩散神经网络的指数稳定性  

Exponential Stability of Stochastic Reaction-diffusion Neural Network with Time-varying Delays

作　　者：张子芳[1] 徐道义[2] 邓谨[2] 

机构地区：[1]淮海工学院数理系,连云港222005 [2]四川大学数学研究所,成都610064

出　　处：《工程数学学报》2008年第2期219-223,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10371083)．

摘　　要：本文是讨论了一类随机变时滞反应扩散Hopfield神经网络的矩指数稳定性。利用平均Lya- punov泛函方法,随机偏微分方程的Ito公式和时滞微分不等式技巧,证明了随机变时滞反应扩散Hopfield神经网络的平衡解的矩指数稳定性,给出了这类随机变时滞神经网络平衡解矩指数稳定性的实用代数判据,得到了一些新结果。最后,给出了主要定理的一个应用实例。This paper discusses the moment exponential stability of a stochastic reaction-diffusion Hopfield neural network with time-varying delays. Using the Lyapunov functional method, the Ito formula of stochastic partial differential equation and a skill of differential inequality with delays, we prove the moment exponential stability of the equilibrium for the stochastic reaction-diffusion Hopfield neural network with time-varying delays. The algebraic criterion of moment exponential stability of the equilibrium for this neural network is obtained. A new result is derived and an example is given to illustrate the main theoretical result.

关 键 词：随机时滞神经网络 反应扩散 时滞微分不等式 指数稳定性 平衡解 

分 类 号：O211.63[理学—概率论与数理统计]