An application of adaptive synchronization of uncertain chaotic system in secure communication systems

Chaotic secure communication via synchronization of chaotic systems has attracted increasing attention in recent years. This note aims to introduce the function projective synchronization (FPS) of coupled fractional-order (FO) complex chaotic Lu system in the master-slave system formalism up to the desired scaling function matrix in the presence of bounded model uncertainties. An efficient chaotic secure communication scheme is proposed using the chaotic masking approach. In order to increase the unpredictability of the information signal, the transmitted signals to the channel are considered as the FO derivative of the product of the information signal and the states of the chaotic system. At the receiver side, by employing the Lyapunov stability theorem, an appropriate adaptive FO control law is derived to synchronize the master and slave systems. After the robust synchronization is achieved, the information signal can be recovered accurately with high speed in the transient response. Finally, to verify the effectiveness of the theoretical results, two numerical simulations are performed and some comparisons based on the adaptation parameter of the control law are provided.