Stability Analysis of a Class of Neural Networks with State-Dependent State Delay

Yue Chen,Jin-E Zhang

doi:10.1155/2020/4820351

Abstract

The differential equations with state-dependent delay are very important equations because they can describe some problems in the real world more accurately. Due to the complexity of state-dependent delay, it also brings challenges to the research. The value of delay varying with the state is the difference between state-dependent delay and time-dependent delay. It is impossible to know exactly in advance how far historical state information is needed, and then the problem of state-dependent delay is more complicated compared with time-dependent delay. The dominating work of this paper is to solve the stability problem of neural networks equipped with state-dependent state delay. We use the purely analytical method to deduce the sufficient conditions for local exponential stability of the zero solution. Finally, a few numerical examples are presented to prove the availability of our results.

Highlights

Neural network is an information processing system to simulate the structures and functions of the human brain
It is proved that the neural network has the ability to approximate nonlinear mapping, and any continuous nonlinear function mapping can be approximated by the multilayer neural network with arbitrary precision
The nerve activity about the structural neural network is worthy of study and discussion from the perspective of models and evolution, and to some extent, the cognitive function of the specific functional neural network is realized by evolutive neurodynamics [13]. e work about evolutive neurodynamics will be helpful to understand the information processing mechanism and the neural energy coding rule in the nervous system and provides the basis for the research of the potential mechanism of cognitive function

Summary

Introduction

Neural network is an information processing system to simulate the structures and functions of the human brain. E processing of neural information involves the coupling and cooperation of multiple levels and regions In this way, the nerve activity about the structural neural network is worthy of study and discussion from the perspective of models and evolution, and to some extent, the cognitive function of the specific functional neural network is realized by evolutive neurodynamics [13]. Hartung [23] described a type of nonlinear functional differential equation with SDSD and analyzed the stability conditions of periodic solutions based on the linearization method. Neural network model with SDSD may interest all those professionals and academics in processing operations who would desire to utilize the capabilities of control systems about capturing rich history information for cost effective and yet robust events to be portrayed.

Preliminaries and Model Description

Main Results

Illustrative Examples

Concluding Remarks