Chaos Synchronization Of Nonlinear Dynamical Systems And Application In Network Systems

Chaos is a kind of widespread phenomenon between nature and human society. It appears a kind of irregular and random movement in the certain system, displaying the complexity of things. Recently, chaos control and synchronization have been intensively studied, and they have become a hot topic in the research field of chaos. In this paper, my dissertation mainly focuses on the chaos control and synchronization and complex networks. And combine together with systems, giving a very valid method to control the systems. The main content is depicted as follows: In the third chapter, the global time-delay synchronization of nonlinear dynamical system is discussed. We addresses a practical issue in chaos synchronization of SQCF system and HCSA system which are based on the Lyapunov stabilization theory and matrix measure, such that the state of the slave system at time t +Ï„is asymptotically synchronizing with the master at time t. The Mathematical software is used to prove the effectiveness of this method. The forth chapter discusses the synchronization of coupled time-varying systems. Based on the Lyapunov stabilization theory and matrix measure, we propose some simple generic criterions of global chaos synchronization between two coupled time-varying systems from a unidirectional linear error feedback approach. These simple criterions are applicable to some typical chaotic systems with types of nonlinearity, such as SQCF system. The Mathematical software is also used to prove the effectiveness. In the fifth chapter, the possibility and development of chaos synchronization in networks are introduced in brief. Under the networks background, which is extensively researched recently, a global chaos synchronization scheme of three coupling nodal state vectors in networks is proposed .The scheme is based on the Lyapunov stabilization theory and matrix measure. How to choose coupling parameter is the key point. By choosing proper coupling parameters, the states of all the three nodal state vectors can be synchronized.