Synchronization Analysis Of Discontinuous Cohen-Grossberg Neural Networks

In nature and human society, because of natural law and the variety of subjectiveand objective factors, discontinuous system widely exists in many practical problems．Many mathematical models of Physics, Electronic Engineering, Artificial Intelligence,Biological and Automatic Control are performance for the ride end discontinuousdifferential equation. In recent decades,based on discontinuous functions, the stabilityand synchronization of neural networks have become the hot topics all over the world.Research on these problems is not only of important theoretical value but also ofpractice significance. Research neural network synchronization,find its internalmechanism can help people have a better understanding of the collective behavior ofnetworks, explain many phenomena in our life and guide the practice. In this thesis, wedeal with the global synchronization of Cohen-Grossberg neural networks withdiscontinuous activation functions by means of Lyapunov functional, matrix theoryand some other skills. Some Sufficient conditions are obtained to guarantee the globalsynchronization of the considered systems. The thesis is divided into five chapters.The first chapter summarizes the research situation and progress of neuralnetworks, discontinuous neural networks and the synchronization issue of neuralnetworlss. And the main work of this thesis is also simply introduced.The second chapter introduces some foundation knowledge necded in this thesissuch as definitions, Lemmas.The third chapter considers the dynamical behaviors of Cohen-Grossberg neuralnetworks with discontinuous activation functions. Based on Lyapunov functional andmatrix theory, we obtain some new sufficient conditions ensuring the globalexponentially synchronization of the considered systems.In the fourth chapter, we study the global exponentially synchronization ofCohen-Grossberg neural networks with delay and discontinuous activation functions.By using Lyapunov functional, matrix theory and inequality analysis, we deduce somesufficient Conditions ensuring global exponentially synchronization of the consideredsystems. Some existing results are improved and extended.In the fifth chapter, we study the periodic synchronization of discontinuousCohen-Grossberg neural networks with delay and periodic coefficients. Sufficientconditions for the periodic synchronization of the considerd systems are established by using Lyapunor functional, matrix theory and differential inequality technique. Whichextend some important results in the literature.