具变时滞细胞神经网络系统解的稳定性与Hopf分岔（英文）  

Stability and Hopf-Bifurcation of Solution for a Cellular Neural Network System with Variable Delays

作　　者：陈宁[1] 田宝单[1] 陈继乾[1] 

机构地区：[1]西南科技大学理学院,四川绵阳621010

出　　处：《生物数学学报》2015年第4期609-619,共11页Journal of Biomathematics

基　　金：Supported by the Natural Science Foundation(No.11ZB192)of Sichuan Education Bureau;the key program of Science and Technology Foundation(No.11Zd1007)of Southwest University of Science and Technology

摘　　要：在本文中,我们利用不动点理论和技巧,结合一类变时滞细胞神经网络系统的动力特征,研究其概周期解的存在性,在传递函数去掉有界的条件下,得到其不依赖于时滞的解的存在唯一性。进一步应用指数D-划分法,讨论系统的平衡点的性态,给出其稳定性和Hopf分岔存在的充分条件.再者我们研究具有时滞随机细胞神经网络系统解的指数稳定性,得到了当该系统的扰动项满足Lipschitz条件时的一些几乎必然指数稳定性的代数准则.In this paper,by using the fixed point theory and techniques of differential inequality,the existence and uniqueness of almost periodic solution,and the dynamic characteristic for a cellular neural networks system with variable delay and studied.The bounded condition of transfer function(activate function) is abandon,and we give that more weak condition not dependent delay.Further,we discuss quality for dynamic system,and by D-divide method for index number of polynomial to study the stable of equilibrium points and the existence of Hopf-Bifurcation that may get some conditions for it.Addition,we discuss the almost sure exponential stability of stochastic delayed cellular neural networks.When perturbed terms in the model of the neural network satisfy Lipschitz condition,some algebraic criteria of almost sure exponential stability are obtained.

关 键 词：细胞神经网络 时滞 概周期解 HOPF分岔 几乎必然指数稳定 

分 类 号：O175[理学—数学]