Research On Two Kinds Of Complex Network Synchronization Problems Based On Discontinuous Control Strategies

In recent years,the research on the behaviors of the complex networks has become a hot topic in the research area of complex networks.This paper focuses on the problem of synchronization of complex networks,.The following is the main works of this paper:The first,chapter briefly introduces the background of complex networks.In the second chapter,to prove the problems we study,some preparatory work related to the synchronization of complex networks must be done,including the introduction of some general mathematical model of complex network,some related definitions of this article and the main results we proved by lemmas,theorems,etc..In chapter 3,the cluster synchronization problem for a class of linearly coupled com-plex networks with nonidentical nodes is concerned based on event-triggered strategies.The event-triggered rules are applied to the coupling terms of the complex networks in order to achieve cluster synchronization.Some simple yet generic criteria of cluster syn-chronizatjion in continuous monitjoring event-triggered rules are obtained by means of the Lyapunov function,algebraic graph theory and differential inequality method.In addi-tion,it is proved that the Zeno phenomenon does not occur under the given constraints.Finally,a numerical example is given to illustrate the complex network can realize cluster synchronization under the two updated rules,which verifies the validity of the theoretical results.In the fourth chapter,the synchronization problem of a class of general hybrid cou-pled networks with time delay and coupling delay and noise is considered.In this chapter,a new impulse cont,rol strategy called the partial mixed impulsive control strategy is pro-posed.In addition,in order to make our model more in line with the actual situation,the network model we designed considers two coupling terms and noise interference,and two coupling terms are delayed coupling term and without delayed coupling term,respective-ly,in which the coupling delayed term also includes communication delay and feedback delay.The derived criterion and convergence rate are closely related to the proportion of the controlled nodes,the strengths of mixed impulses,the impulsive intervals,the time delays and the topology structure of the networks.Finally,a numerical example is given to demonstrate the effectiveness of our results.The last,chapter is the conclusion of this paper,which briefly summarizes the main research work of this paper.