| Complex network has caused a considerable interest in the study of science and engineering, with the rapid development of computer science and network theory, which becomes a new researching focus in recent years. Because a lot of complex networks exist in our daily life, such as Internet, WWW, metabolic network, social network, energy-supplying network, transportation network, information network, finance network and so on, all of those are greatly associated with daily life. Study on the dynamic behavior of complex networks such as stability and synchronization is help for people to completely understand and apply it in aspect of theory and practice. In this paper, my dissertation mainly focuses on the adaptive control and synchronization of the complex network. The main content is depicted as follows:In Chapter 1, the background, significance, current situation and content of the research are introduced briefly.In Chapter 2, the conceptions of complex dynamical network are introduced. Correlative researching outcomes recently at home and abroad concerning synchronous issues about complex dynamical network have been analyzed.In Chapter 3, adaptive control and synchronization of the complex dynamical network with non-delayed coupling is studied. By using the Lyapunov stability theory and the well-known LaSalle invariant principle on dynamical system theory, some synchronous conditions were derived. Numerical simulation is presented to demonstrate the feasibility and effectiveness of the techniques.In Chapter 4, based on stability theory on delayed dynamical systems, two different kinds of new adaptive controllers have been designed for the complex dynamical network with non-delayed and delayed coupling. Some generic criteria are derived for synchronization of such dynamical network. Illustrative simulations are provided to verify the synchronization of a dynamical network composing of three nodes. The results of the numerical simulations are compatible with the theoretical analysis.
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