Synchronization Of Complex Dynamical Networks With Nonlinearly Coupled Nodes

In the literature of study on complex dynamical networks, the inner-couplings are often assumed to be linear. Very little research work concerned the nonlinear coupling networks. However, in many practical networks, the interplay of two different nodes in a network can not be described accurately by linear functions because they are naturally nonlinear functions. A concrete example is cellular neural networks in which the neurons are coupled by the linear combination of their nonlinear activation functions. In all previous studies, when considered the state nonlinear coupling chaotic complex dynamical networks, they all used the state control method. But the state variables of a node are the multi-dimensional vector, so using this state control method will take up a lot of resources in the actual communication engineering network. Furthermore, generally only partial state variables can be directly measured. This dissertation investigates the locally and globally synchronization of nonlinearly coupled complex dynamical networks. Unlike the existing synchronization methods, the nodes’outputs of a complex network are used to construct synchronization controllers. The main contributions are as follows:Firstly, considering the complex dynamical network with nonlinear coupling, we use each node’s output variable to design the controller. Synchronization criteria are achieved for this complex dynamical network on the basis of the Lyapunov stability theory. Using the Lorenz system as a node of the network, numerical simulations are given to demonstrate the effectiveness of the proposed method.Secondly, we extend the above method to state nonlinear coupling complex dynamical networks with coupling time-delay. The linear output controller is constructed for the synchronization of such networks, and the control parameters are designed based on Lyapunov theory.Thirdly, we study the synchronization of uncertain state nonlinear coupling complex dynamical networks. The output control method is applied to design the adaptive controller, and the synchronization criteria for this complex network are obtained.Finally, considering the complex dynamical network with nonlinear coupling, the pinning control method using the node’s output variable is proposed. The criteria for choosing control parameters are obtained based on Lyapunov stability theory. Some simulations are given to demonstrate the effectiveness of the proposed method and criteria.