Synchronization In Complex Dynamical Networks

Complex networks have been intensively studied in many fields, from physics and neurobiology to engineering and social sciences. The complexity in networks is generally inherent and comes from both structures and dynamics. In this thesis, the author mainly focuses on the control and synchronization in dynamical complex networks. The main content is as follows:After an introduction and summary of the research background and current status of the control and synchronization of dynamical complex networks, the synchronization of the regular network, random network, small-world network and scale-free network are introduced. And also, Synchronization criterion of continuous time coupled dynamical complex network is discussed.To deal with the time-delay property of network, a more general time-delay dynamical network model is presented. After an unstable fixed point is supposed to exist, we adopted the time-delay feedback control method and the standard feedback control method to acquire the error of the system. According to the Lyapunov theorem, a sufficient condition of the stability of the network is presented by a condition of a linear matrix inequality (LMI) in terms of a parameter matrix associated with network. And then a numerical simulation example is provided to verify the theoretical results.The links in some complex networks system are either connected or disconnected, such as a electric power system, communication system etc. Moreover synchronization of these complex networks is related to the connective quality of the nodes. Therefore, we introduce a kind of more general complex dynamical network model. This model emphasizes on connective relationship between the nodes and we further investigate its synchronization property. Based on the network model, we show that the synchronization of the complex dynamical networks is determined by means of link matrix, the eigenvalues and the corresponding eigenvectors of coupled matrix for a uniform network. Especially, when the connection quantity is exceeding a certain value, the complex network will achieve stabilization.