| Synchronization study of complex network is the one of the most active areas of complex network study at present. The synchronization of complex network can explain many complex phenomena in nature, and close contact with the real world. Therefore, synchronization study of complex network has some practical significance and wide applications. The research progress of complex network is recapitulative introduced in this thesis, including established complex network models, the features of network, the significance of network synchronization and research status at home and abroad. At the same time, two criterions of the synchronization of complex network:Master stability function criterion and Lyapunov function criterion are described, as well as several typical reported examples of the complex network synchronization are introduced. On this basis, Lyapunov function is constructed by backstepping design for single variable coupling connections, and the spatiotemporal chaos synchronization in chain network with topology equipollence is investigated. Taking the Gray-Scott spatiotemporal chaos system as an example, the simulation results show that the synchronization principle is feasibility. In this method, only one controller is added at the terminal node of complex network and synchronization of the entire network can be achieved, meaning the low-cost synchronization and convenient practical applications. In addition, the spatiotemporal chaos synchronization in tree network with different structure is studied in our work based on the Master stability function criterion. The condition for complex network synchronization is obtained by determining the largest Lyapunov index of the network. The Panfilov, Fitzhugh-Nagumo and Plankton spatiotemporal chaos systems are taken as network nodes, respectively, numerical simulation results show the effectiveness of the method.
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