Stability And Synchronization Analysis Of Complex Dynamical Networks With Proportional Delay

This thesis mainly studies the dynamics of complex dynamical networks with proportional delay.(1)Neural network is a kind of special and widely used complex network.We will study the stability of a kind of neural network with proportional delay;(2)Synchronization is a typical group behavior of complex networks.Impulses and delays exist in complex networks and affect the synchronization of networks.Therefore,we will study the synchronization of a class of complex networks with impulses and proportional delays.This paper consists of four chapters:As an introduction,The first chapter introduces the purpose and significance of the research,the related research status at home and abroad.The second chapter discusses the stability of a class of neural networks with proportional delay.By proposing a Lyapunov-Razumikhin method,some delay-dependent conditions are established to guarantee global power stability of a class of differential equations with proportional delay.Finally,three examples are presented to illustrate the validity of the obtained results.In third chapter,the synchronization problem of a class of coupled complex networks with proportional delay and impulse is discussed.Firstly,under irregular impulse,the concept of“logarithmic average impulse interval”is proposed,according to the monotonicity and boundlessness of proportional delay function,a unified criterion for synchronization in complex networks with proportional delay is derived,which is valid for both synchronous and asynchronous impulses.Secondly,founded on the viewpoint of impulsive control,by a known impulsive differential inequality in proportional delay,the impulsive control problem for synchronization of complex networks is studied,a suitable impulsive controller is designed to guarantee the synchronization of complex networks with proportional delay.Since the obtained conditions are expressed by linear matrix inequalities(LMIs),it is feasible in practical problems.Lastly,two numerical examples are given to illustrate the availability of our results.Chapter four summarizes our work and puts forward some problems for future research.