Synchronization Of Complex Networks Via Delayed Impulsive Control

With the deepening of the degree of social information,complex networks are ubiquitous.Many things in life can be formulated by complex networks,such as,neural networks,power grids,communication networks,food chain,world wide web,and so on.In some degree,these applications represent the dynamic study of complex network models.As a vital class dynamic behaviors,synchronization has attracted widespread attention due to its wide applications in various fields,such as pattern recognition,secure communication,image process,and so on.There are many control strategies proposed by many professors,where impulsive control,as a class of discontinuous control method,is more robustness and security.In secure communication,it has some particular advantages.In addition,in the process of network transmission,due to the limited transmission rate,the collection and processing of information cannot be completed instantaneously,which leads to the fact that the time delay phenomenon is inevitable.Hence,the study on driveresponse synchronization of time delay complex networks with delayed impulse control has become one of the important research directions in this field.In this paper,the delayed impulsive synchronization control problem of complex networks with time delay is studied.The outline of the rest of this paper is as follows:In Chapter 1,we firstly introduce the background and significance which are involved by this paper,the main research content of this paper,and some important lemmas which are needed to be used.In Chapter 2,impulsive differential inequality is developed and generalized.Firstly,impulsive differential inequality involving distributed delayed impulse is established.Based on the theory of impulsive control and the Razumikhin method,the solution of the inequality and its exponential decay rate are estimated.In addition,we further develop and generalize impulsive differential inequality and consider the case of unknown-bound time delay.Combined with ?-function,the solution of the inequality is estimated.As a importantly theoretical tools,the proposed results shall be applied to the delayed impulsive synchronization of complex networks and the design of controller.In Chapter 3,the problems on distributed delayed impulsive synchronization of chaotic neural networks and the design of controller are studied.Firstly,we consider a class of chaotic neural networks.By applying the obtained distributed delayed impulsive differential inequality and using the Lyapunov method,a distributed delayed impulsive controller is designed for the response system of chaotic neural networks such that the response system is exponentially synchronized with the drive system,where the effect of distributed delay in impulse is fully considered.Finally,two numerical examples are presented to illustrate the effectiveness of the obtained results.In Chapter 4,we consider a general complex networks with coupling structures and time delay.The delayed impulsive synchronization control problem of the complex networks is studied.We consider the case that the bound of time delay is unknown.Based on the obtained delayed impulsive differential inequality,some sufficient conditions are established to achieve the ?-synchronization between the drive system and the response system.Finally,a numerical example is presented to illustrate the effectiveness of the obtained results.