Graph-theoretic Approach To Stability And Synchronization Of Cohen-grossberg Neural Networks

It’s well known that Cohen-Grossberg neural network has broad applications inmany fields, including parallel computation, signal processing, associate memory etc.This kind of neural network becomes the focus in academia just because of its widelyapplication. Various methods are put forword by scholars to study its dynamic behaviorsuch as line matrix inequality method, Lyapunov method, M-matrix theory and othermethods. Combining graph theory with Lyapunov method, stability and synchronizationof a stochastic time-delay Cohen-Grossberg neural network with reaction-diffusion termare discussed in this paper. The relationship between topological structure of the systemand its dynamic behavior is considered in graph theory.In the first part of this paper, the p-th moment exponential stability of a stochastictime-delay Cohen-Grossberg neural network with reaction-diffusion term is studied.Every neuron in the Cohen-Grossberg neural network system is considered as a vertexand directed arcs are uesd to denote connections between neurons. Thus, the system canbe represented by a directed graph. Then, p-th moment exponential stability of theCohen-Grossberg neural network system can be researched by using Lyapunov methodand graph theory. Some criteria for p-th moment exponential stability, which are closelyrelated to topological properties of the system, are given in this part. Finally, thecorresponding numerical example is given to verify the validity of the results.In the second part of this paper, the p-th moment exponential synchronization ofthe system which we have considered above is investigated. First of all, an error systemis derived by the difference between driving system and response system. Then,inequality technique, graph theory and Lyapunov stability theory are used to investigatethe p-th moment exponential stability of the error system, some criteria for which arereceived in this part. That is, criteria for p-th moment exponential synchronization ofdriving system and response system are obtained. Similarly, the validity of the argumentis illustrated through the corresponding numerical example.