Periodic Solutions of Cohen-Grossberg-Type BAM Neural Networks with Time-Varying Delays

Qiming Liu,Shaoning Li

doi:10.4236/ijcns.2012.512085

Abstract

Sufficient conditions to guarantee the existence and global exponential stability of periodic solutions of a Cohen-Grossberg-type BAM neural network are established by suitable mathematical transformation.

Highlights

Many important results on the existence and global exponential stability of equilibria of neural networks with time delays have been widely investigated and successfully applied to signal processing system
The dynamic behavior of periodic oscillatory solution is very important in learning theory [1,2], which is motivated by the fact that learning usually requires repetition, some important results for periodic solutions of Hopfield neural networks or Cohen-Grossberg neural networks with delays have been obtained in Refs. [3,4,5,6,7,8,9,10,11,12,13,14,15]
The objective of this paper is to study the existence and global exponential stability of periodic solutios of a class of Cohen-Grossberg-type BAM neural networks (CGBAMNNs) with time-varying delays by suitable mathematical transformation

Summary

Introduction

Many important results on the existence and global exponential stability of equilibria of neural networks with time delays have been widely investigated and successfully applied to signal processing system. The research of neural networks involves the dynamic analysis of equilibrium point and that of periodic oscillatory solution. The dynamic behavior of periodic oscillatory solution is very important in learning theory [1,2], which is motivated by the fact that learning usually requires repetition, some important results for periodic solutions of Hopfield neural networks or Cohen-Grossberg neural networks with delays have been obtained in Refs. The objective of this paper is to study the existence and global exponential stability of periodic solutios of a class of Cohen-Grossberg-type BAM neural networks (CGBAMNNs) with time-varying delays by suitable mathematical transformation. Sufficient conditions which guarantee the existence and global exponential stability of periodic solutions for the CGBAMNNs are established Section 3.

Preliminaries

Periodic Solutions of CGBAMNNs with Time Varying Delays

An Example