The Study Of Synchronization For Chaotic Systems And Complex Networks

This paper is devoted to the study of synchronization for chaotic systems and complex networks. Firstly, a brief description of historical background and research progress for chaos, complex network and synchronization is given. Secondly, the research work of the paper is introduced. The research focuses mainly on five parts:(1) Generalized synchronization between two continuous dynamical systems is discussed. By exploring the Lyapunov stability theory and constructing appropriately unidirectional coupling term, a sufficient condition for determining the generalized synchronization between continuous systems is proved. Two examples are used to show the effectiveness of this result.(2) Generalized synchronization between two different dimensional chaotic dynamical systems possesses significance in the research of synchronization. In order to study it, we propose an approach to achieve generalized synchronization between two different dimensional chaotic systems based on the Lyapunov stability theory. This method can be used widely. Numerical examples are given to demonstrate the effectiveness of this approach.(3) The problem of synchronization between two different chaotic systems is investigated. An generic adaptive synchronization scheme is proposed for a class of chaotic systems with uncertain parameters. Based on Lyapunov stability theorem, two adaptive controllers and corresponding parameters update laws are designed to synchronize two chaotic systems. Numerical simulations are also given to show the effectiveness of the proposed method.(4) The problem of synchronization in complex dynamical networks is investigated. Based on the stability theory of impulsive differential equations, an impulsive control scheme is proposed to achieve impulsive synchronization for complex dynamical networks with unknown coupling. The synchronization strategy considers the influence of all nodes in the dynami- cal network and the effect intensity of every node to network synchronization relies on it's weight in the network. For practical problems, by choosing appropriately the weights of the nodes in the network, network synchronization can be achieved by only a few useful nodes. Simulated examples are provided by using the chaotic Chua system as nodes of the dynamical network, and the effectiveness of the proposed impulsive control are demonstrated.(5) The study of synchronization for dynamical network with discrete coupling is very significative. Based on the theory of matrix analysis and the stability theory of impulsive differential equations, we propose an approach to achieve complete synchronization for a class of dynamical network with discrete coupling. Numerical simulations are also given to show the effectiveness of the proposed approach.At last, the work of this dissertation is summarized and the prospective of future research is discussed.