New Results for Periodic Solution of High-Order BAM Neural Networks with Continuously Distributed Delays and Impulses

Chang-Bo Yang,Ting-Zhu Huang,Jin-Liang Shao

doi:10.1155/2013/247046

Abstract

ByM-matrix theory, inequality techniques, and Lyapunov functional method, certain sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential stability of periodic solution for a new type of high-order BAM neural networks with continuously distributed delays and impulses. These novel conditions extend and improve some previously known results in the literature. Finally, an illustrative example and its numerical simulation are given to show the feasibility and correctness of the derived criteria.

Highlights

As is well known, during the hardware implementation of neural networks, time delays are inevitable due to finite switching speeds of the amplifiers and communication time, which may bring about complex influence on the system such as oscillation and instability [1, 2]
Impulsive effects wildly exist in many realistic networks [3, 4], which may be caused by witching phenomenon, sudden changes, or other unexpected noise
Due to its wide application in pattern recognition, associative memory, image, and signal processing, Bidirectional associative memory (BAM) neural networks with delays and impulses have been extensively studied in the past few decades [15,16,17,18,19,20,21,22]

Summary

Introduction

As is well known, during the hardware implementation of neural networks, time delays are inevitable due to finite switching speeds of the amplifiers and communication time, which may bring about complex influence on the system such as oscillation and instability [1, 2]. Due to its wide application in pattern recognition, associative memory, image, and signal processing, BAM neural networks with delays and impulses have been extensively studied in the past few decades [15,16,17,18,19,20,21,22]. We will consider a new type of highorder BAM neural networks with continuously distributed delays and impulses, which can be described by the following integrodifferential equations: dxi (t) dt m. Huo et al [29] and Yang [30] studied the existence of periodic solution and its exponential stability for an impulsive highorder BAM neural network with discrete delays by using the theory of coincidence degree and Lyapunov functional method.

Preliminaries

Main Results

An Example

Conclusions