Study On Several Synchronization In Complex Dynamical Networks

In recent years, complex network has been widely applied in various fields. The complex network of scientific theory also provides a solid theoretical and technical foundation for the booming technology networks, network engineering, protection and development of applications, so the theory of complex networks is still a hotspot for various scholars. The main concern in this thesis is the synchronization of different complex networks. Based on the Lyapunov stability theory, the networks achieve different types of synchronization state by using different control methods.The first chapter introduces the research background and research status of complex networks, some common types of synchronization and control methods, as well as related concepts and Lemma. In second chapter, the outer synchronization of a complex network with double non-delayed and double delayed coupling is investigated. Combined with linear matrix inequality, drive response system achieves synchronization in the role of non-linear controller according to the decomposition technique of coefficient matrix. Simulation shows the matrix decompositions method can reduce the conservatism of the system to a certain extent. The third chapter, unlike most of the literature, this section selects a complex network with non-identical nodes of different dimensions. In order to realize the sufficient conditions of synchronized network, an adaptive controller and parameter adaptive rate are well designed. In chapter four, a novel synchronization scheme, generalized dislocated function projective synchronization(GDFPS) in two different dimensional complex networks, is proposed. The states of two complex networks with different orders are asymptotically synchronized up to a desired scaling function. Due to the special nature of the scaling function of this synchronization type, which covering other special types of projective synchronization, the study of this part is more general. In numerical simulations, the nodes in each network have different dynamics. The simulation results verify the effectiveness and feasibility of the proposed synchronization method.