Novel Criteria of ISS Analysis for Delayed Memristive Simplified Cohen–Grossberg BAM Neural Networks

Yong Zhao,Shanshan Ren

doi:10.1155/2020/3612394

Abstract

The memristor as the fourth circuit element, it can capture some key aspects of biological synaptic plasticity. So, it is significant that the characteristic of memristors is considered in neural networks. This paper investigates input-to-state stability (ISS) of a class of memristive simplified Cohen–Grossberg bidirectional associative memory (BAM) neural networks with variable time delays. In the sense of Filippov solution, some novel sufficient criteria for ISS are obtained based on differential inclusions and differential inequalities; when the input is zero, the stability of the total system is state stable. Furthermore, numerical simulations are illustrated to show the feasibility of our results.

Highlights

In 1988, Kosko proposed a class of bidirectional associative memory (BAM) neural networks [1]
Because of potential applications of associate memory and pattern recognition, many research studies are increasingly concerned about dynamics behaviors of such neural networks. ere have been many results on the stability for BAM neural networks with or without delays [2,3,4,5,6,7,8]
Zhong et al [29] obtained some sufficient conditions for the input-to-state stability of a class of memristive neural networks with time-varying delays

Summary

Introduction

In 1988, Kosko proposed a class of bidirectional associative memory (BAM) neural networks [1]. Zhao et al [28] considered the input-to-state stability of a class of memristive Cohen–Grossberg-type neural networks with variable time delays, which include some known results as particular cases. Zhong et al [29] obtained some sufficient conditions for the input-to-state stability of a class of memristive neural networks with time-varying delays. Zhao et al [30] discussed dynamics of memristive BAM neural networks with variable time delays and obtained some novel sufficient conditions of the inputto-state stability. From these papers, we know the input-to-state stability is general stability.

Preliminaries

Main Results

A Numerical Example

Conclusions