Global Robust Exponential Stability and Periodic Solutions for Interval Cohen-Grossberg Neural Networks with Mixed Delays

Yanke Du,Rui Xu

doi:10.1155/2013/963897

Abstract

A class of interval Cohen-Grossberg neural networks with time-varying delays and infinite distributed delays is investigated. By employing H-matrix and M-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions are established for the existence, uniqueness, and global robust exponential stability of the equilibrium point and the periodic solution to the neural networks. Our results improve some previously published ones. Finally, numerical examples are given to illustrate the feasibility of the theoretical results and further to exhibit that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system admits rich and complex dynamics.

Highlights

In the past two decades, neural networks have received a great deal of attention due to the extensive applications in many areas such as signal processing, associative memory, pattern recognition, and parallel computation and optimization
In [4,5,6], employing homeomorphism techniques, Lyapunov method, H-matrix and Mmatrix theory, and linear matrix inequality (LMI) approach, Shao et al established some sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for the following interval Hopfield neural networks: n ui (t) = − diui (t) + ∑aijfj (uj (t))
Motivated by the works of [4,5,6] and the discussions above, the objective of this paper is to investigate the global robust exponential stability and periodic solutions of the following Cohen-Grossberg neural networks (CGNNs) with time-varying and distributed delays: ui (t) = − αi (ui (t))

Summary

Introduction

In the past two decades, neural networks have received a great deal of attention due to the extensive applications in many areas such as signal processing, associative memory, pattern recognition, and parallel computation and optimization. Motivated by the works of [4,5,6] and the discussions above, the objective of this paper is to investigate the global robust exponential stability and periodic solutions of the following CGNNs with time-varying and distributed delays: ui (t) = − αi (ui (t)). A concluding remark is given in Section 6 to end this work

Preliminaries

Global Robust Exponential Stability of the Equilibrium Point

Periodic Solutions of Interval CGNNs

Numerical Simulation

Conclusion