Stability of Delayed Hopfield Neural Networks with Variable-Time Impulses

Yangjun Pei,Qi Han,Chao Liu

doi:10.1155/2014/154036

Abstract

In this paper the globally exponential stability criteria of delayed Hopfield neural networks with variable-time impulses are established. The proposed criteria can also be applied in Hopfield neural networks with fixed-time impulses. A numerical example is presented to illustrate the effectiveness of our theoretical results.

Highlights

Hopfield neural networks [1], which were referred by Hopfield in 1984, have attracted many attentions of researchers and have been applied in many fields such as pattern recognition, associative memory, and combinatorial optimization
Up to now, the vast majority of stability results for impulsive Hopfield neural networks are focused on the case of fixed-time impulses
We focus on the destabilizing effects of Hopfield neural networks with variable-time impulses

Summary

Introduction

Hopfield neural networks [1], which were referred by Hopfield in 1984, have attracted many attentions of researchers and have been applied in many fields such as pattern recognition, associative memory, and combinatorial optimization. Many researchers have investigated impulsive Hopfield neural networks and have obtained many interesting stability results [11,12,13,14,15,16,17,18,19]. Up to now, the vast majority of stability results for impulsive Hopfield neural networks are focused on the case of fixed-time impulses. In [20], we have focused on BAM neural networks with variable-time impulses and have obtained some crucial theoretical results. We focus on the destabilizing effects of Hopfield neural networks with variable-time impulses.

Preliminaries

Main Results

Numeric Example