Synchronization Of Complex Spatiotemporal Networks With Topology Switching Characteristics

The potential application value of complex network synchronization has been widely concerned by people.In the practical process of the synchronization in the network,there are many unpredictable factors,especially when some nodes fail or add new nodes,the structure of the network will be greatly changed,which leads to the failure of the synchronization state of the last stage.Obviously,the topology of the network at each switching time has a crucial impact on the synchronization of the network.Therefore,the research on complex network synchronization problem with switching topology characteristics has a very important theoretical and practical value.The first chapter briefly introduces the research background of complex dynamical networks,network models and synchronization methods.In this chapter,several kinds of networks and their dynamic switching synchronization processes are briefly introduced.At the same time,we briefly introduce the research significance of network synchronization and its development trend at home and abroad.The second chapter mainly introduces some necessary mathematical preparation knowledge.In addition,we also list some typical spatiotemporal chaotic models which are used to construct the network.Finally,several network synchronization methods are introduced.In the third chapter,the problem of projective synchronization between different spatial and temporal networks with uncertain scaling factors is studied.Based on the Lyapunov stability theory,we not only identified the network synchronization controller structure and the underlying factor recognition law,but also avoid to solving dynamic network coupling matrix of the second maximum of the eigenvalues to obtain the conditions of network synchronization.Finally,we use the Predator-Prey space-time model and the Gray-Scott space-time model as the target network and the nodes of the response network,and the effectiveness of the synchronization scheme is verified by numerical simulation.In the fourth chapter,we extend the synchronization control scheme of the third chapter to the discrete variable structure space-time network,and discuss the problem of the synchronization of discrete-time switching networks with unknown parameters.Based on the stability theory,we design a special positive function to construct the network of the Lyapunov function,so as to obtain the structure of space and time synchronization network conditions.Meanwhile,the uncertain parameters of the dynamic equation of the network nodes are identified effectively by designing the identification law of the uncertain parameters.Finally,the network is simulated by the coupled map lattice model.