Studies On Synchronization And Control Of Complex Networks

Recurrent the study of synchronization and anti-synchronization of complex networks, which have been extensively studied in mathematics, complexity science, physics, biology, computer science and so on. The main reason lies principally in that recurrent complex networks have complicated dynamic behavior, including periodicity, chaos and so on. In order to enable complex networks to achieve synchronization or anti-synchronization, we need to add the appropriate controller such as adaptive controller, feedback controller and so on. So, this paper mainly studies the synchronization and controller of recurrent complex networks.This paper has six parts.Chapter 1 summarizes the development of complex networks, the current status and meaning of dynamics of recurrent complex networks, while introducing the main contents and originalities of this paper.Chapter 2 investigates impulsive synchronization of complex delayed dynamical networks with nonsymmetrical coupling. Based on impulsive control theory on delayed dynamical systems, some generic criteria for synchronization are established by constructing Lyapunov functional and design suitable impulsive controller of the proposed control methodology. Furthermore, the outcomes of the chapter include or improve part of the conclusions drawn from the existing literatures.Chapter 3 analyzes adaptive-impulsive synchronization of uncertain dynamical networks. Some sufficient conditions ensuring the globally asymptotical synchronization and exponential synchronization of two identical networks are obtained by using Lyapunov function method combined with the impulsive analysis. Two numerical examples are exploited to demonstrate the feasibility and applicability of the proposed synchronization approaches. The outcomes of the chapter improve part of the conclusions drawn from the existing literatures.Chapter 4 consists of the discussions of the anti-synchronization of delayed drive system and response system neural networks. Based on matrix measure and inequality, exponential anti-synchronization of a class of chaotic networks with time-varying delays is investigated. The outcomes of the chapter improve part of the conclusions drawn from the existing literatures.Chapter 5 studies the exponential anti-synchronization of a class of delayed chaotic neural networks with impulsive. By constructing Lyapunov functional, and using LMI method, some new criteria for the global exponential anti-synchronization is obtained. We imposed feedback control and impulsive control to enable the network to achieve anti-synchronization, and also discussed the two kinds control to impact the speed of anti-synchronization. The outcomes of the chapter improve part of the conclusions drawn from the existing literatures.In the last chapter, the essay concludes the research work of this paper, and looks forward to the future research directions.