Outer Synchronization Between Two Time-delay Complex Dynamical Networks Under Pinning Control

In this dissertation, the outer synchronization between two complex dynamical networks isaddressed. Considering both the influence of time delay arised in the communication process andtwo complex dynamical networks with different node-dynamics, the synchronous controller ofcomplex dynamical networks is designed under pinning control to get two complex dynamicalnetworks synchronization. The main research work and achievement are as follows:First, for the output coupled time-delay complex network model, the outer synchronizationbetween two complex dynamical networks is addressed. Under pinning control, a feedbackcontroller is proposed by using output signals of partial nodes to get outer synchronization betweentwo complex dynamical networks. The controller parameters are designed based on Lyapunovstabilization theory. Simulations are given for global coupling network, the nearest neighborcoupling network, the BA scale-free network and the WS small-world network, showing theeffectiveness of the proposed method.Second, for the state coupled time-delay complex network model, the outer synchronizationbetween two complex dynamical networks is addressed. A feedback controller is proposed by usingoutput signals of partial nodes and by pinning control method to get outer synchronization betweentwo complex dynamical networks. The criteria for choosing control parameters are obtained basedon Lyapunov stability. Numerical simulations are given for typical networks and the resultsdemonstrate the effectiveness of the proposed method.Third, the outer synchronization control issue is addressed between two complex networks withdifferent node-dynamics. State coupling and output coupling complex network models areconsidered respectively. A feedback controller is proposed by using output signals of partial nodesand by pinning control method to get the synchronization. How to choose control parameters arebased on Lyapunov stability. Taking the Lorenz’s system and Lüsystem as the nodes of drivingnetwork and response network respectively, numerical simulations are given for typical networks.The results demonstrate the effectiveness of the proposed method. Through the simulations, theselection methods under pinning control are analyzed and compared for different networktopologies, further demonstrating the effectiveness of the proposed method.