具有时滞的细胞神经网络吸引集与周期解存在性

Existence of Attracting Sets and Periodic Solutions for Cellular Neural Networks with Delays

本文利用Lyapunov函数法并结合不等式分析技巧,在不要求时滞细胞神经网络神经元的输出函数满足全局Lipschitz条件下,证明了时滞细胞神经网络的正不变集与吸引集的存在性,同时给出周期解的存在的充分条件。本文还构造了吸引集,使得周期解有了较明确的几何范围。

This paper studies the delayed cellular neural networks in which the neural output functions do not satisfy the Lipschitz condition. According to the Lyapunov function and the method of inequality analysis, the existence of positive invariant sets and attracting sets, and the sufficient condition for the existence periodic solution of this system are obtained. By constructing the attracting sets, a quite obvious geometric position for periodic solution is determined.