Synchronization And Consensus Of Several Classes Complex Networks

In the survival of human society,with the rapid development of social information,complex networks are closely related to our lives.The research of complex network has not only profound theoretical significance but also practical value.As one of the most important research content in network science,the dynamic behavior of complex networks is the product of the reciprocal chiasmata of network topology and differential equations,so it has important theoretical and practical value.As the most typical phenomenon in complex networks,synchronization and consensus are used in many disciplines and engineering applications.In the study of synchronization and consensus of complex network,for the convenience of the study,researchers usually make various assumptions of individual dynamics and network topology,however in practice the individual dynamics and network topology are more complicated,therefore there are a lot of problems to be solved in the study of synchronization and consensus of complex network.Based on previous studies,the paper study the synchronization and consensus problems of multi-agent systems by using graph theory,matrix theory and dynamical system theory.In the part of research of synchronization,this paper improves the hypothesis of individual dynamics,.and in the part of research of consensus,this paper considers the more complicated network topology,on the other hand,this paper consider system of fractional order dynamics equation.Specifically,this paper is divided into six chapters,the first and second chapter briefly describe the research background and current situation of synchronization and consensus of complex networks,then introduces some preliminary results related to the research content;from the third chapter to the fifth chapter the main results are established,in the end,in the sixth chapter the work is summarized and the future research work is prospected.The main results are as follows.1.This third chapter investigates exponential synchronization of linearly coupled ordinary differential systems.First,it gives a new method to analyze the exponential synchronization of the systems.Second,two theorems and their corollaries are proposed for the local or global exponential synchronization of the coupled systems.Finally,an application to the linearly coupled Hopfield neural networks and several simulations are provided for the effectiveness of the theoretical results.2.This fourth chapter investigates the finite-time consensus problems of multi-agent systems with continuous time-varying interaction topology,in order to simplify the study,only considering the undirected topology.A distributed consensus protocol is presented to make the multi-agent system locally or globally reach consensus in finite time,according to graph theory,finite time stability theory.Then,the shortest time of the system is estimated and the inequality condition is given.The protocol is also used to analyze finite-time consensus of the multi-agent systems with fixed or modified switching topologies.Numerical simulations are presented to illustrate the effectiveness of the obtained results.3.With the development of the fractional calculus,many natural phenomena in the system with fractional order dynamics can be well explained,and in many engineering systems,compared with the integer order model,fractional derivative model can accu-rately simulate the dynamic process of the system,so the fifth chapter is devoted to the study of consensus of fractional-order multi-agent systems via distributed nonlin-ear protocols over a directed interaction graph.Its dynamical behaviors are described by fractional-order differential equations.Based on graph theory,matrix theory and properties of fractional-order calculus,the sufficient conditions are given to guarantee consensus via nonlinear protocols.Then,consensus to prescribed value is also solved.Finally,simulations are given to show the validity of the theories.