Hopfield神经网络模型全局稳定的弱条件

A Weak Condition for the Hopfield Neural Networks

研究了Hopfield神经网络模型全局渐近稳定的弱条件.模型中的激活函数没有有界和可微的限制,并且右上Dini导数可在多点取得最大值.首先构造Lyapunov函数,并利用可分析方法,证明了系数矩阵半负定是全局渐近稳定的弱条件.然后,通过例子和数值模拟说明了结论的有效性,改进了已有文献的结论.

This paper studies the weak condition for the Hopfield neural networks whose activation may not be bounded or differentiable, and furthermore the upper right Dini derivatives of activation may obtain the maximum at more than one point. Firstly, by Lyapunov function and analysis methods condition of globally asymptotic stability is proposed. Then, example and numerical simulations are illustrate the theory developed in this paper. Our theory improves the existing results in the literature. functions functions , a weak given to