Research On Complex Dynamical Networks And Its Synchronization

Currently, research on complex networks just begins to emerge and attracts much attention. In fact, complex networks are on our life nowadays. In the paper, we apply theories of nonlinear dynamics, statistical physics, matrix analysis, and use computer calculating method to study synchronization on complex networks. Based on relational network models, we analyze the effects of topology and weight distribution of a network on complex network. These researches have great significance for the understanding and practical applications of the synchronization in real networks.The paper can be divided into three parts. In the first part, we discuss the research background of the complex networks theory and its fundamental theory, such as the networks' topological parameters, the mean shortest path-length, the clustering coefficient, the maximal load of the link in the networks, etc. We also discuss some basic networks topologies, which have been widely studied and also serve as the base of our research work.Furthermore, we introduce the synchronization on complex network after introducing the properties of complex network. We make use of several models, such as SIR, SIS, to study the synchronization in complex networks, then, we study the criterion of synchronization in different network.. After that, we propose what the criterion is in different networks, regular network, small-world network, scale-free network for example. The properties and the synchronization of the complex networks are prepared for improving the synchronization.At last, we propose several methods to improve the synchronization in the complex networks, such as MZK and so on. Using these methods, the synchronization is remarkably improved.