Synchronization Control Strategy Research Of Directed Complex Network Based On Spanning-tree

In recent years, with the discovery of small-world networks and scale-free networks,more and more researchers begin to study complex networks. We can see lots of complexnetworks in our daily life, for example, the Internet, nerve network and biological networks.The research of complex network involves lots of cross-disciplines, such as nonlinear theory,control theory, graph theory.Complex network can be divided into directed network and non-directed network,depending on their coupling mode. The control of complex network consist of global controland pinning control, the former means adding controllers to all of the nodes, the latter meansadding controllers to part of the nodes. For the non-directed complex network, there has beena lot of strategies to select the controlled nodes, such as the strategy based on connectiondegree, the strategy based on betweenness centrality, the strategy based on local betweennesscentrality.In reality, most of the complex networks are directed networks, the researches ondirected complex networks are still on the beginning. As the adjacency matrix of directedcomplex network is non-symmetric, there are lots of differences between directed complexnetwork and non-directed complex network. From these different characteristics of thedirected complex network, the control of it will be studied in this paper.In this paper, the main research objects are some common network models. Two differentalgorithms are proposed, one is under the condition of sufficient coupling strength, and theother has no limitation on the coupling strength. State feedback controller was used tosynchronize the directed complex networks, whose nodes are Chen’s oscillator model. Thispaper can be divided into the following five parts:The first part briefly describes the background and significance of this research, theresearch history and the recent research findings of complex networks are also brieflyoverviewed.The second part gives a basic concept of the complex network and the mathematicalmodel of the node. And then, the dynamical mathematical model of network and some basicconcept of synchronization are described.Part three makes a controllability analysis of the complex network. An algorithm isproposed and its comparison with other algorithms is made briefly. Also, two simulations aremade to verify the algorithm.In the fourth part, analyses of the network topology and network parameters are made. At last, the algorithm was improved to remove the restriction; a simulation was made toverify the conclusion too. Then a summary of the article was made.