Synchronization Of Small World Networks With Differend Structures

Complex network can be seen everywhere in life.Complex network synchronization is widely used in the power systems,security systems,the Internet and so on.So it has great significance impact to master the modeling and the characteristics of complex network synchronization on the theoretical research and actual work.In this paper,NW small world network as a model,respectively,it is achie ved that internal synchronization of a smal-world network and external synchronization of two small-world networks.First of all,the Lyapunov direct method and the Lyapunov theorem are introduced,based on the Lyapunov theorem,the controller is set up to realize the chaos synchronization between a R?ssler attractor and a Lorenz attractor.On this basis,a NW small-world network with 20-node is constructed,the first node's state equation is R?ss ler's one and the others are Lorenz's equations.Only in the coupling,the network does not achieve synchronization;Based on the Lyapunov stability theorem to set the controllers,after the controllers are added to the nodes whose state equations are Lorenz equations,the network reaches synchronization,and the number of nodes has no effect on the synchronization of the entire network.Finally,it is constructed that a 12-node NW small-world network with different structure,in which the first node's state equation is R?ssler's one and the others are Lorenz's equations.It is constructed that a 10-node NW small-world network,in which the nodes' state equation are Lorenz's equations.Based on the Lyapunov stability theorem,the controller is set up.Controllers are added to the nodes whose state equations are Lorenz equations,which realize the out-synchronization of the two small-world networks.The number of nodes in the two networks has no influence on the synchronization of the whole network.