Study Of The Synchronization For Some Complex Dynamical Networks With Time Delay

A complex network is defined as a large set of coupled interconneted nodes by edges, in which a node is a fundamental unit having specific contents and exhibiting dynamical behavior, typicality. In recent years, complex networks have been considered as a new subject and many domestic and foreign scholars, including phyics, biology, mathematics and information technology, etc., have placed extensive emphasis on this subject. Many complex systems, from the actual background, such as the Internet, the World Wide Web, the power grid, railway networks, and so on, can be described by complex dynamical networks. The ultimate aim of studying complex networks is to understand how topological properties have an effect on the dynamical behavior. Synchronization, one of the typical collective behaviours of complex dynamical networks, has received rapidly increasing attention from different fields in recent years. Based on the research of synchronization in complex networks, on the one hand, we can understand how topological properties affect synchronous ability, on the other hand, we can enhance the synchronous ability of networks when synchronization is advantaged, and reduce its negative factors. Therefore, synchronization of complex networks provides with great theoretical significance and potential applications.Since time delays are ubiquitous in natural, so in the practical complex networks, time delays ofen exist in the state variables or coupling coefficients. In this dissertation, stability theory of time delay system, control theory and matrix theory are introduced into the study of complex networks. Synchronization analysis of several classes complex dynamical networks with time delay has been proposed. The main research work of this thesis has several parts as follows:In the first section, we introduce the research background, some fundamental knowledge and basic concepts of nonlinear dynamical systems and complex networks. And we also summarize some present work on the synchronization and control of complex dynamical networks which are related to the topic of the thesis. Finally, the research work of this paper is presented.In chapter 2, we mainly investigate the problem of projective synchronization for complex networks with time delay. Firstly, Topology identification and parameters identification are challenging work in complex networks. Adaptive projective synchronization between two complex networks with time-varying coupling delay is investigated by the adaptive control method, and this method has been applied to identify the exact topological structure and uncertain parameters of a weighted general complex network. Secondly, the projective synchronization of drive-response time-varying complex networks is investigated. We consider synchronization in time-varying coupling networks, in which the weights of links are time varying. A hybrid control method, that is, an adaptive feedback controller with impulsive control effects is designed. From numerical simulation results, we find the impulsive control or adaptive control effect is not as well as the adaptive-impulsive control strategy.In chapter 3, in reality, if network nodes are of similar properties, we can regard it as one network; otherwise, as two or more networks. Synchronization of two general complex dynamical networks with non-delayed and delayed coupling is investigated by using an adaptive-impulsive control. Based on the stability analysis of impulsive differential equation, the criteria for the synchronization are derived, and a linear impulsive controller and the simple updated laws are designed simultaneously. Particularly, the weight configuration matrix is not necessarily symmetric or irreducible, and the inner coupling matrix need not be symmetric.In chapter 4, In much of the literature, time delays in the couplings are considered; however, the time delays in the dynamical nodes, which are more complex, are still relatively unexplored. Therefore, in this paper, Outer synchronization of two coupled complex network with nonidentical time-delayed dynamical nodes is considered via using linear feedback control and adaptive control, respectively.In chapter 5, this paper investigates the synchronization between two linearly coupled complex networks via pining control method, including inner synchronization inside each network and outer synchronization between them simultaneously. Based on the Lyapunov stability theory and LaSalle's invariance principle, some sufficient conditions for the synchronization are derived, and the controllers are designed.At last, some meaningful results are summarized in the end of this paper. Also some existing problems as well as the future work are pointed out.