The Research Of Chaos Synchronization And Its Applications

In the past decade, the topics of chaos synchronization and parameter estimation have attracted great attention in the field of nonlinear science due to its potential of practical applications. Some techniques for chaos synchronization and parameter estimation have been developed. However, the generalized synchronization in bidirectionally coupled chaotic systems lacks investigation. In our previous work , we propose a new strategy of adaptive synchronization to evaluate all parameters of hyper-chaos systems, and adopt conditional entropy of symbolic dynamics to study generalized synchronization in bidirectionally coupled systems. Our paper is organized as follows. The first chapter mainly reviews the developed history of chaos theory and its basic characteristic. The methods of calculating Lyapunov exponent have been briefly introduced. In the second chapter, some definitions of chaos synchronization and typical synchronization methods at last decade have been reviewed. The applications of chaos synchronization in parameter estimation from time series have been introduced. We point out the existing problems under investigations of chaos synchronization. In the third chapter, we introduce our work. There are some problem in parameter estimation,for example, the adaptive controller seems to be a little complex or the synchronization response rate is not so quickly, and so on.. For a large class of chaotic systems we give an analytical and systematic procedure to estimate dynamically all model parameters form time series. we adopt the following update law: ε_ i =-γ_ie_i~2, q_mj =-δ_mje_mf_mj(y), q_kj =-λδ_kje_kf_kj(y) to estimate all parameters of 4d-LC oscillators and hyper-rossler oscillators。The numerical results show that all model parameters can be estimated from two time series and the method has strong robust。In the fourth chapter We adopt conditional entropy of symbolic dynamics to study bidirectionally coupled R o&& ssler-Lorenz and R o&& ssler-R o&& ssler。First give a criterion of generalized synchronization, i.e. we obtain the conditional entropy by using some coarse representation .we show that the conditional entropy has a sharp minimum with the shift of time parameter when the generalized synchronization is implemented. As an application, we calculate the conditional entropy of rossler-rossler and rossler-lorenz systems. The numeric results show that conditional entropy has a sharp minimum when there is a generalized synchronization between the two systems.,the transition point appears correspond with the second Lyapunov exponent transits from positive to zero。...