Study On Chaos Synchronization Between Complex Networks

Since the famous "seven bridge problem" has been proposed in the 18th century, the theory of complex network has become a hotspot in scientific research after its two centuries'development. A large number of complex networks exist in reality, such as transport network, Internet, interpersonal relationships, biosphere and so on. Many statistic characters have been found in complex networks after scientific work in different fields. The structure of complex networks is complicated, and the nonlinear dynamic behavior is different in complex networks with different structures. Nonlinear dynamic behavior is extremely rich and the trend is not easy to predict, therefore, how to get the essential features of the complex networks and make a better use of them has become a key point in the study of complex networks, in which, network synchronization is one of the main directions. The basic concept of complex networks, together with the contents and the significance of research are presented in this paper and synchronization between complex networks are further studied. Global synchronization between complex networks with different nodes is first studied and two-dimensional chaotic systems are used to construct different nodes of complex networks. The error equations between the variables of two nodes in the networks are designed based on the Lyapunov stability theory, and global synchronization between two complex networks is realized. Ring network with the unified chaotic system as nodes and star network with hyperchaotic R(o|¨)ssler system as nodes are taken as examples, and simulation is made to show the effectiveness of the method. Network synchronization of nonlinear coupling continuous spatiotemporal chaos is studied on the basis. Linear configuration is made according to the linear item of the spatiotemporal chaos systems, nonlinear coupling method is presented between networks is designed based on Lyapunov stability theory, the error equation is got, and spatiotemporal chaos synchronization between networks is realized. The Kuramoto- Sivashinsky continuous spatiotemporal chaos systems are used as nodes. Unidirectional ring net work and star-network are taken as example to verify the effective of the method.