不具备全局利普希茨条件的时滞分流抑制型细胞神经网络的伪概周期解  

Pseudo almost periodic solutions of delayed shunting inhibitory cellular neural networks without Global Lipschitz Activaty Functions

作　　者：张红[1] 

机构地区：[1]湖南文理学院数学与计算科学学院,湖南常德415000

出　　处：《湖南文理学院学报（自然科学版）》2013年第3期1-5,共5页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：湖南省教育厅科研资助项目(11C0915)

摘　　要：研究了不具备全局利普希茨条件的时滞分流抑制型细胞神经网络系统,得到其伪周期解存在性及其唯一性的充分条件,推广并改进了早期有关这方面研究的结果.通过构造Lyapunov函数并利用Banach压缩映像原理,得到本系统具有指数型稳定性的伪概周期解的充分条件.In this paper, shunting inhibitory cellular neural networks are studied. Without assuming the global Lipschitz conditions of activaty functions, some new sufficient conditions are obtained for ensuring the existence and uniqueness of pseudo almost periodic solution of this system. Our results improve and generalize those of the previous results. Furthermore,several methods are applied to establish sufficient criteria for the exponential stability of this system. The approaches are based on con-structing suitable Lyapunov functionals and the well-known Banach contraction mapping principle.

关 键 词：指数型稳定 LYAPUNOV函数 伪概周期解 分流抑制系统 

分 类 号：O175.14[理学—数学]