Synchronization Between Two Complex Dynamical Networks With Non-Identical Topological Structures

The recent decade has witnessed great development in the study of the theory and applications of complex networks, which has attracted much attention and become one of the hot research topics. Diversity of the structure and the dynamical behaviors of complex networks make the research more meaningful and challenging. The study on the network synchronization has been an important topic in control theory and engineering field.Based on complex dynamical network coupled by outputs, the synchronization between two complex dynamical networks is studied in this dissertation, considering both cases of identical and non-identical network topological structures. The main contents the dissertation contain the following several parts:Firstly, complex dynamical network models are reviewed briefly, and the outer synchronization of both output-coupling and state-coupling complex dynamical networks with identical topological structures is analyzed.Secondly, considering the time-delay in the realistic networks, an approach for synchronization between two or more dynamical complex nerworks is proposed using scalar signals, and then is extended to the networks coupled with state variables. Based on Lyapunov Stability theory, several useful criteria for synchronization are given. Some illustrative examples with Lorenz sysytems are given to demonstrate the effectiveness of the proposed method.Thirdly, the synchronization between two output-coupling complex dynamical networks with non-identical topological structures is studied. As the topological structures of complex dynamical networks are completely given, the simple feeback control scheme is proposed using scalar signals. Adaptive synchronization is also proposed for the networks with uncertain topological structures, and then is extended to the networks with time-varying coupling delay. Simulations are given to verify the effectiveness of the proposed approach.