Projective Synchronization of Driving–Response Systems and Its Application to Secure Communication

In this paper, we first introduce the model of single-driving double-response system (SDDRS), which consists of a driving system (subsystem) and two response systems (subsystems). By applying the theory of Lyapunov stability, we study the projective synchronization of SDDRS between the driving and response systems. The sufficient conditions for achieving projective synchronization are obtained when the driving system has either a globally stable equilibrium point or a chaotic attractor. Furthermore, we use the SDDRS for cryptography in secure communication and present a novel scheme for encryption and decryption based on its projection synchronization. The results of numerical simulations verify the efficiency of the presented control schemes and the excellence of cryptography.