On Synchronization Control Method For Multi-network Based On Leader-Follower Model

Many complex systems in the real world can be modeled as complex networks and then analyzed and described.Nowadays,as an important research direction in the field of complexity science,complex networks theory is applied to more and more scientific fields,such as computer,social science,biology and physics and so on.At present,studies on the synchronization of complex networks are almost carried out for a single network.However,in the reality,any network is not isolated,and they are coupled to each other to form more complex multi-network system.Therefore,it is valuable and significant to study synchronization method for multi-network.In this thesis,Lyapunov stability theory and Kronecker product are used to study multi-network synchronization.The main work can be summarized as follows.Firstly,for the multi-network system based on the leader-follower model,the mathematical model is established for the leader network and follower network in the multi-network system respectively.A negative feedback controller is designed and proved by Lyapunov stability theory to obtain sufficient condition for synchronization of multi-network.Some numerical simulations are carried out on multi-network system consisting of small-world network and scale-free network respectively,and the simulation results verify the validity of the conclusion.In multi-network system,different pinning nodes can get different synchronization effect.The pinning nodes are selected with degree centrality,closeness centrality,betweenness centrality and eigenvector centrality as the standards respectively,and negative feedback controllers are applied.By numerical simulations,multiple-network system can get shorter synchronization time by selecting the pin nodes with degree centrality as the standards.Secondly,a multi-network system with time delay is considered,the mathematical models with time-delay are established for the leader network and the follower network in the multi-networks system respectively.A suitable controller is designed and proved by Lyapunov-Krasovskii stability theory to obtain sufficient condition for synchronization of multi-networks with time-delay.Some numerical simulations are carrried out on multi-network system consisting of small-world network and scale-free network respectively,and the simulation results verify the validity of the conclusion.Finally,the research work of this thesis is summarized,and the future research direction of multi-network synchronization is prospected.