含脉冲的随机延迟细胞神经网络的均方指数稳定性与周期解（英文）  

Mean Square Exponential Stability and Periodic Solutions of Stochastic Delay Cellular Neural Networks with Impulses

作　　者：李浩[1] 李毓[2] 

机构地区：[1]广西师范大学数学与统计学院,桂林541004 [2]信阳师范学院经济学院,信阳464000

出　　处：《工程数学学报》2016年第1期91-105,共15页Chinese Journal of Engineering Mathematics

基　　金：The Major Project of Foundation of Educational Committee of Henan Province(14B910001);the Planning Project of Philosophy and Social Science of Henan Province(2014BJJ069)

摘　　要：本文主要研究一类带离散延迟和脉冲的随机细胞神经网络(SDCNNsw I)的均方指数稳定性和周期解的存在性.首先,用庞加莱收缩理论分析了SDCNNsw I的周期解存在条件;其次,用李雅谱诺夫函数、随机分析理论和Young不等式推出了几个定理,给出了保证SDCNNswl的周期解具有均方指数稳定性的几个充分条件,其中只包含SDCNNsw I的几个控制参数,通过简单的代数方法即可验证.最后,通过两个例子说明了所提出准则的有效性.For a class of stochastic cellular neural networks with discrete delays and impulses （SDCNNswI）, this paper discusses their exponential stability and the existence of periodic solutions. Firstly, Poincare contraction theory is utilized to derive the conditions to guarantee the existence of periodic solutions of SDCNNswI. Next, Lyapunov function, stochastic analysis theory and Young inequality are developed to derive some theorems. These theorems provide several sufficient conditions to guarantee that the periodic solutions of SDCNNswI are mean square exponentially stable. These sufficient conditions only include the governing parameters of SDCNNswI and can be easily checked by simple algebraic methods. Finally, two examples are given to demonstrate the usefulness of the obtained results.

关 键 词：布朗运动 YOUNG不等式 ITO公式 李雅谱诺夫函数 指数稳定性 细胞神经网络 

分 类 号：O193[理学—数学]