A Complex Network Synchronization Issues

This paper founds a class model of complex networks with local interaction and studies the synchronization phenomenon of this network. The complex network with local interaction means that the control input make all nodes arrive at synchronization object, according to the feedback information between any node and its neighbors. The feedback infonnation of any node with its neighbors is more precisely than that of the node with others, so the synchronization speed be faster. From the graph theory, the topo logical structure of the network is complete graph in existed results, but the topological structure is connected graph in our network. From above analysis, this class complex network is more realistic and general. Based on these advantages, this paper is start.At first, we consider the complex network model with pinning control. Based on this complex network model, we analyze the synchronization stability of this network and have this conclusion: based on the pinning control, all nodes of the network will reach a synchronization state in limited time, and concerning this synchronization state are asymptotically stable. We also give and prove some network synchronization standards in form of linear matrix inequality (LMI). Furthermore, under some assumptions, we give some simulations in 2-D and 3-D space respectively.Then, we consider the complex network model with inner-coupling interaction and time-varying delays. Based on the synchronous target in control input with and without time-varying delay, we consider the synchronization of the complex network for node and its neighbors all with variable delays, and we have the result: if the time-varying delays satisfy some matrix inequalities conditions, the complex network will achieve at synchronization target. Furthermore, under some different topological structures and time delays, we give some simulations.Finally, based on the above model, we research the synchronization of the complex network for node without delay, but its neighbors with time-varying delay. Similar to the above analysis, based on the synchronous target in with and without time-varying delay, and we have the result: if the time-varying delays satisfy some matrix inequalities conditions, the complex network will achieve at synchronization target. Furthermore, we give some simulations.