Research On Problems Of Synchronization On Chaotic Systems And Complex Networks

During the past 20 years, nonlinear science has made vigorous development. The research on it not only has significance of science, but also has good banausic prospects. Chaos is an important branche of nonlinear science, has been widely studied and applied. Especially, chaos synchronization received great concern from scholars. The research on various synchronizations has become hot issues of nonlinear science area. For example, completely synchronization, generalized synchronization, phase synchronization and so on. Chaos synchronization has showed good prospects of application in many areas, such as mathematics, information science, communications security, biological engineering and medical science. In this article, two normal kinds of chaos synchronization are studied: completely synchronization (CS) and generalized synchronization (GS).The development and origin of chaos, definition of chaos, characteristics and classification of chaos, chaos control, theory and methods of chaos synchronization are presented in the introduction. The relevant contents and progress of GS and CS are intruduced. Then this dissertation is devoted to the study on synchronization for a class of chaotic systems. The research includes adaptive generalized synchronization in partially linear chaotic systems, synchronization in a time-varying coupling strength network, numerical simulations are given. At last, the conclusions of the paper and the prospects are given. The specific works are as follows:(1) For partially linear drive-response chaotic systems, by designing a simple adaptive controller, drive system and response system can be achieved generalized synchronization. The stability of generalized synchronization is proved based on Lyapunov stability theory. The result of simulations is in agreement of the theorem.(2) A new scheme to synchronize a time-varying coupling strength complex network is proposed. It has been proved by using the well-known LaSalle invariance principle that the state of such a complex network can synchronize easily without knowing the synchronization trajectory. Numerical results show the validation of the proposed synchronization algorithms.For the above studies, we use Matlab to obtain simulation results.The results of simulations are in agreement with the theorms.