Generalized function projective synchronization of chaotic systems for secure communication

By using the generalized function projective synchronization (GFPS) method, in this paper, a new scheme for secure information transmission is proposed. The Liu system is employed to encrypt the information signal. In the transmitter, the original information signal is modulated into the system parameter of the chaotic systems. In the receiver, we assume that the parameter of receiver system is uncertain. Based on the Lyapunov stability theory, the controllers and corresponding parameter update rule are constructed to achieve GFPS between the transmitter and receiver system with uncertain parameters, and identify unknown parameters. The original information signal can be recovered successfully through some simple operations by the estimated parameter. Furthermore, by means of the proposed method, the original information signal can be extracted accurately in the presence of additional noise in communication channel. Numerical results have verified the effectiveness and feasibility of presented method. Mathematics subject classification (2010) 68M10, 34C28, 93A30, 93C40