时滞Hopfield神经网络全局渐近稳定的弱条件  

A Weak Condition of Globally Asymptotic Stability for Hopfield Neural Networks with Time Delays

作　　者：宿娟 SU Juan(Department of Mathematics, Chengdu Normal College, Chengdu 610044, Sichuan)

机构地区：[1]成都师范学院数学学院,四川成都610044

出　　处：《四川师范大学学报（自然科学版）》2018年第3期381-386,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省教育厅自然科学一般项目(18ZB0094);四川省教育厅自然科学重点项目(15ZA0135)

摘　　要：研究时滞Hopfield神经网络全局渐近稳定的弱条件,其中系统的激活函数没有有界和可微的限制,比S型的要求更弱.首先构造一个Lyapunov函数,计算得到沿系统解的右上Dini导数非正,从而获得平衡点的局部稳定性.然后利用反证和分析方法,进一步证明该Lyapunov函数在时间趋于无穷时的极限为0,从而获得平衡点的全局吸引性.结合局部稳定性和全局吸引性,说明系统是全局渐近稳定的,且平衡点唯一.This paper studies the weak condition of globally asymptotic stability for Hopfield neural networks with time delays. The activation functions employed in the system may not be bounded or differentiable,which are less constrained than the S type. Firstly,by constructing a Lyapunov function,I calculate its upper right Dini along the solution of the system. The non-positivity of the derivative under the restraint of parameters of the system indicates that the equilibrium of the system is locally stable. Then by the analysis method,the limit of the Lyapunov function is proved to be 0 as time approaches infinity. Thus,the global attractivity of the equilibrium is obtained. Together with the local stability and global attractivity of equilibrium,we derive a sufficient condition of globally asymptotic stability of the system,which implies the uniqueness of equilibrium.

关 键 词：HOPFIELD神经网络 时滞 全局渐近稳定 弱条件 

分 类 号：O29[理学—应用数学] TP183[理学—数学]