时间尺度上的高阶Hopfield神经网络的概周期解

Almost periodic solution of high-order Hopfield neural networks on time scales

研究了时间尺度上带有连接项和分布时滞的Hopfield神经网络的概周期解.利用时间尺度上动力系统的指数二分性和Banach不动点定理,给出了系统存在唯一的概周期解的充分条件,即系统在满足(H_1)^(H_4)的条件下,进一步假设α<1成立,则系统有唯一的概周期解.这个结果在很大程度上推广和延伸了以前的相关结果.

In this paper, almost periodic solution of high-order Hopfield neural networks with leakage term and distributed delays on times scales is proposed. By applying the exponential dichotomy of linear dynamic system and Banach＇ s fixed point theorem on time scales, some sufficient conditions for unique almost periodic solution of this sys- tem are obtained ： suppose that the condition （H1） - （H4 ） are fulfilled and further assume that a 〈 1 is satisfied, then there is an unique almost periodic solution for this system. This result improves and extends the ones in the previous works to a large extent.