Matrix Measure Approach for Stability and Synchronization of Complex-Valued Neural Networks with Deviating Argument

Wenbo Zhou,Biwen Li,Jin-E Zhang,Sanbo Ding

doi:10.1155/2020/8877129

Abstract

This paper concentrates on global exponential stability and synchronization for complex-valued neural networks (CVNNs) with deviating argument by matrix measure approach. The Lyapunov function is no longer required, and some sufficient conditions are firstly obtained to ascertain the addressed system to be exponentially stable under different activation functions. Moreover, after designing a suitable controller, the synchronization of two complex-valued coupled neural networks is realized, and the derived condition is easy to be confirmed. Finally, some numerical examples are given to demonstrate the superiority and feasibility of the presented theoretical analysis and results.

Highlights

Recurrent neural networks have always been an object with immense attention due to their specific self-learning ability, which makes neural networks have been extensively applied in combinatorial optimization, signal processing, parallel computing, and some other fields [1,2,3,4,5,6,7,8]. ese widespread applications of neural networks are practically based on their affluent dynamic properties in theory, including stability, synchronization, dissipativity, and chaos. erefore, some researchers have become more interested in the theoretical study about the dynamical behaviors of neural networks and achieved lots of excellent works [9,10,11,12,13,14,15,16,17,18]
complex-valued neural networks (CVNNs) could be regarded as an expansion about the real-valued neural networks (RVNNs) in a certain sense, in which the state variable, activation functions, and synaptic strength matrices are all complex-valued. erefore, such networks have much more sophisticated features than the RVNNs in many aspects and make it capable to settle a lot of matters that cannot be settled by the real-valued ones [19]
It is very significant to research the dynamical behaviors of CVNNs, especially the stability and synchronization

Summary

Introduction

Recurrent neural networks have always been an object with immense attention due to their specific self-learning ability, which makes neural networks have been extensively applied in combinatorial optimization, signal processing, parallel computing, and some other fields [1,2,3,4,5,6,7,8]. ese widespread applications of neural networks are practically based on their affluent dynamic properties in theory, including stability, synchronization, dissipativity, and chaos. erefore, some researchers have become more interested in the theoretical study about the dynamical behaviors of neural networks and achieved lots of excellent works [9,10,11,12,13,14,15,16,17,18]. In [36], the matrix measure approach is used to study the stability behaviors of CVNNs with time-varying delays, and several stability conditions are obtained based on the Halanay inequality. Motivated by the above discussions, we try to use matrix measure approach to analyze global exponential stability and synchronization for CVNNs with deviating argument. E main results about this paper have been organized as follows: (1) Matrix measure approach is used firstly to analyze the dynamic behaviors of CVNNs with deviating argument, which is susceptive about the sign of the system matrix entries, more efficient and convenient to dispose the network.

Preliminaries

Main Results

Illustrative Examples