Impulsive Synchronization Of Some Complex Dynamic Networks With Time Delays

Synchronization is a common phenomenon in nature and human society, and has received wide attention from scholars in various fields of biological, chemical, medical, aerospace, social and economic. Especially synchronization of complex networks is very important. Research on synchronization of complex network not only has important academic value but also has a broad application base. Since time delay is ubiquitous due to the impact of the actual network distance, limited signal transmission speed, node competition, channel congestion and memory effects and other factors. Hence considering synchronization of delayed dynamic network is more realistic. In addition, impulse control as a classic control method, which has simple structure, low cost and robustness, have been widely used in engineering. Based on Lyapunov stability theory, impulsive delayed differential equations and comparison theorem, this dissertation studies synchronization of delayed complex dynamic networks.Firstly, a complex dynamic network model with time delays both in nodes and coupling is proposed. Pinning control strategy, which means that only a small fraction of the network nodes is controlled, is applied to study impulsive synchronization of complex delayed dynamic networks. Controlled nodes are selected based on error magnitude of their own state and the target state. Several synchronization criteria are obtained for symmetric and asymmetric delayed dynamic networks which are proved to be less conservative by introducing the definition of the average impulsive interval. Finally, simulation examples are given to verify the validity of the results.Secondly, impulsive synchronization of complex dynamic networks with distributed delays is discussed. In some cases, the signal propagation of network is not instantaneous, then a distributed delay is more general to model mechanism of signal transmit. The comparison theorem is extended into the distributed delayed case. Based on Lyapunov function, linear matrix inequality, Jensen inequality and Kronecker product, several synchronization criteria are obtained. The effects of the distributed delay on synchronization are further studied. Finally, a small-world network with chaotic systems as single node dynamic is considered to verify the theoretical results. Finally, impulsive synchronization of heterogeneous dynamic networks is studied. Because each node has a different dynamic behavior, there is neither an equilibrium nor a synchronous manifold in general case. It is difficult to achieve complete synchronization. Instead, a bouned synchronization error will be obtained. By introducing the weighted average of the states of all nodes as the virtual target trajectory, an impulsive controller is designed and sufficient conditions of synchronization are obtained and synchronization error is estimated. Moreover, the theoretical results are supported by numerical simulation.