Synchronization Of A Class Of Chaotic Systems

As one of the important subdisciplines in nonlinear science, chaos theory has a wide range of appliaciton in secure communication and other fields. Compared with the low-dimensional chaotic systems, hyperchaotic system has two or more positive Lyapunov exponent. As the hyperchaotic system with higher security, higher efficiency and many other advantages, there are wide applications in the non-linear circuits, security communication, and neural network etc.. As far as we know, most of the research only considered the identical chaotic systems with known parameters or systems with same order. However, in practical sometimes systems with different order should be considered. Therefore, heterogeneous systems have gradually become a research hotspot. The thesis has studied several synchronization methtods in chaotic system using the theoretical method and numerical simulation:Adaptive control and synchronization of Lu system with known or unknown parameters has been studied. Based on Lyapunov stability theory, an adaptive controller is designed. With the strictly theoretical proved method, the Lii system with known or unknown parameters can be controlled to the stability and achieve self-synchronization.Three synchronization methods:linear feedback method, nonlinear feedback method and impulsive control method were used respectively to study the self-synchronization problem of Lii chaotic system. Based on Lyapunov stability theory and impulsive control method, it theoretically gives the sufficient condition to achieve self-synchronization.Based on state observer method, a generalized projective synchronization scheme has been proposed which also has been theoretically proved to drive a class of hyperchaotic systems get generalized projective synchronization. The effectiveness of the proposed approach is validated by numerical simulations of two well-known hyperchaotic systems: hyperchaotic Lii system and hyperchaotic Rossler system.Full state hybrid projective synchronization (FSHPS) in two non-identical chaotic systems with same or different order has been studied. Based on the Lyapunov stability theory, an adaptive controller is designed and the parameter update law is presented. It is proved theoretically that the controller can not only make two non-identical systems with same order asymptotically achieved FSHPS, but also apply to systems with different order by using the system expansion method. In numerical simulations, the FSHPS between two chaotic systems with same order (Loren and Chen-lee systems) and different order (hyper chaotic Lii system and Chen system, Lii system and hyper chaotic Rossler system) are presented to show the effectiveness of the proposed scheme.