Synchronization Of Three Classes Of Time-varying Complex Dynamical Networks

The complex dynamical networks have been widely applied in many fields,meanwhile,there are many problems and phenomena in complex dynamical networks that need to be studied.Synchronization phenomena have been widely observed in nature and man-made system,thus have been studied for decades.There are many different patterns of synchronization since there are many factors that can influence the synchronization.Synchronization of three classes of time-varying complex dynamical networks are studied in this paper,and adaptive method is used to realize synchronization.This thesis is composed by six chapters.In chapter 1,we introduce the complex dynamical networks and its application,and related research status are given in this part.In chapter 2,we give some concepts and useful lemma.The main results are given in chapter 3-5.In chapter 3,the time-varying lag synchronization between two complex dynamical networks is studied.Lag time is an important factor that affect the lag synchronization,and lag time was usually fixed.In this chapter,considering time-varying lag time,time-varying lag synchronization is proposed with unknown change rate of lag time.Controllers are designed to achieve the time-varying lag outer synchronization and conclusion is proved.Simulation example is given to show that the controllers can be applied effectively.In chapter 4,the passivity and output synchronization of complex dynamical networks with unknown coupling strength are addressed,and an adaptive coupling scheme is proposed.The sufficient condition for the passivity of complex dynamical networks with different dimension of input and output is given,and a sufficient condition for the output synchronization of the complex dynamical networks is derived.Numerical simulations are provided to demonstrate the correctness of the proposed scheme.In chapter 5,the cluster synchronization of complex dynamical networks with unknown time-varying coupling strength by pinning control is studied,where the dynamic of nodes in different cluster is different.Adaptive pinning controllers are designed to realize the cluster synchronization,and the trajectory of pinning nodes synchronize with the target trajectory.Numerical simulations are presented to demonstrate the results.We summarize the contributions and limitations of this paper,and give some further improvement directions in chapter 6.