Research On Synchronization Methods Of Chaotic Systems

The chaos theory occupies an important position in the nonliner research field. Chaos research is very closed with the research in biological, chemical and other research feilds. In recent years, a substantial number of the research in control and synchronization field of the time chaos exists. At the same time, people pay more attention to the spatiotemporal chaos because of its high simulation in time and space.We did the theoretically derived of the research in. the control and synchronization of the chaotic systems based on the numerical simulation. the main works are as follows:.(1) Research on the generalized synchronization chaotic systems using coupled map lattices (CML). Generalized synchronization of two coupled map lattices is realized through feedback control method and appropriate range of feedback parameters. Based on this method, phase compression extends the range of the parameters. The combine of feedback control and phase compression implement generalized synchronization and reduce the qualification of it effectively. Numerical simulations show the effectiveness and the feasibility of the proposed program.(2) We use the non-linear coupled method to implement the synchronization of two coupled map lattices. Through the separation of the linear and nonlinear terms of the spatiotemporal chaotic systems appropriately, we set the nonlinear term as the coupling function and then we can achieve the synchronization of two coupled map lattice. After that, we implement the secure communication of digital image using this synchronization method. Then, the discrete characteristics of the nonlinear coupling spatiotemporal chaos act on the discrete pixel of the digital image. After the synchronization of the both communication parties, the receiver can decrypt the original image. Numerical simulations show the effectiveness and the feasibility of the proposed program.(3) This paper studies the synchronization and anti-synchronization of the spatiotemporal chaos based on the control parameters.Compared to the other spatiotemporal chaos research modes, we select the coupled map lattice as the example of the research on the spatiotemporal chaos. Based on Lyapunov stability theorem, we select appropriate control parameters respectively, then we can achieve the synchronization and anti-synchronization of the two coupled map lattice systems. At the same time by selecting the appropriate coupled map lattice parameters, numerical simulations show the effectiveness and the feasibility of the proposed program. (4) We research on the adaptive synchronization of the hyper-chaotic systems. We use the adaptive control method with the parameters unknown and propose a new adaptive controller which is common and useful. We use the Lyapunov stability theory to demonstrate that the controller can realize the synchronization of the hyper-chaotic systems with the parameters unknown. The following numerical simulations show the effectiveness and the feasibility of the proposed program.