Exponential Stability of Periodic Solutions for Inertial Type BAM Cohen-Grossberg Neural Networks

Chunfang Miao,Yunquan Ke

doi:10.1155/2014/857341

Abstract

The existence and exponential stability of periodic solutions for inertial type BAM Cohen-Grossberg neural networks are investigated. First, by properly choosing variable substitution, the system is transformed to first order differential equation. Second, some sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov functional and using differential mean value theorem and inequality technique. Finally, two examples are given to illustrate the effectiveness of the results.

Highlights

The Cohen-Grossberg-type BAM neural networks model is initially proposed by Cohen and Grossberg [1], has their promising potential for the tasks of parallel computation, associative memory, and has great ability to solve difficult optimization problems
In the following we only prove that (11) has one ω-periodic solution, which is exponentially stable
We prove that (u∗T(t), V∗T(t))T is a solution of system (3)

Summary

Introduction

The Cohen-Grossberg-type BAM neural networks model is initially proposed by Cohen and Grossberg [1], has their promising potential for the tasks of parallel computation, associative memory, and has great ability to solve difficult optimization problems. The authors Ke and Miao [20, 21] investigated stability of equilibrium point and periodic solutions in inertial BAM neural networks with. Ke and Miao [23] investigated the stability of inertial Cohen-Grossberg-type neural networks with time delays. To the best of our knowledge, the question on the periodic solutions of inertial type BAM Cohen-Grossberg neural networks with time delays is still open. To provide the theoretical basis of practical application, this paper is devoted to present a sufficient criterion to ensure the existence and exponential stability of periodic solutions for inertial type BAM Cohen-Grossberg neural networks with time delays. We consider the following inertial type BAM CohenGrossberg neural networks with time delays: d2ui (t) dt[2].

Preliminaries

Main Results

Numerical Examples

Conclusion