Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications

Abstract

This paper is concerned with the existence and global exponential stability of the periodic solution of delayed Cohen–Grossberg neural networks (CGNNs) with discontinuous activation functions. The activations considered herein are non-decreasing but not required to be Lipschitz or continuous. Based on differential inclusion theory, Lyapunov functional theory and Leary–Schauder alternative theorem, some sufficient criteria are derived to ensure the existence and global exponential stability of the periodic solution. In order to show the superiority of the obtained results, an application and some detailed comparisons between some existing related results and our results are presented. Finally, some numerical examples are also illustrated.

Exponential Synchronization of Cohen-Grossberg Neural Networks With Delays

“…In recent decades, CGNN has attracted much attention due to its potential and widespread applications in the fields of pattern recognition, model prediction, optimization problems, signal processing. The realization of neural networks depends on their dynamic behavior, such as stability, convergence, oscillation and periodicity, and many research results have also appeared [2], [3], [4], [5], [6], [7], [8], [9], [10]. Time delay may result from the onset of non-vanishing oscillations and may affect the dynamic behavior.…”