| Synchronization control of chaotic systems has been one of the most active areas in the chaotic theory. Especially, the projective synchronization (PS) has become the hotspot during last decade and found its many potential applications in secure communication and information engineering, etc, duo to its unpredictable characteristics of scaling factor. The projective synchronization, firstly proposed by Mainieri and J. Rehacek in1999, developed rapidly recent years and many types of synchronization have been proposed, for example, the modified projective synchronization(MPS), the function projective synchronization(FPS), modified function projective(MFP), etc.In this paper, the definition of chaos, chaos control and synchronization introduced firstly. Then, some typical methods of chaos synchronization and the works of recent years for chaos synchronization control are summarized, including the generalized projective chaos synchronization for the chaotic systems with anti-symmetric structure, the projective synchronization by a linear coupling function, the projective synchronization via active sliding mode control and the lag projective synchronization via impulsive control, etc. This works proposed a method to synchronize the projective synchronization of two different systems for constant scaling factor with nonlinear feedback gain control method. For a class of chaos systems, nonlinear functions are separated from the error dynamics system properly and a nonlinear feedback gain controller is designed, in which the feedback gain matrix elements are derived based on Lyapunov’s direct method. The results are verified by the numerical simulations on the Lorenz system and Chen system. It can be seen that the feedback gain matrix depends on scaling factor, the parameters of drive system and the attractor size of the response system. This method can be applied to synchronize the modified projective synchronization between two different chaos systems. |
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