Complete synchronization and projective lag synchronization of complex-valued hyperchaotic Lorenz system and Lü system via active control

This paper studies the complete synchronization (CS) and projective lag synchronization (PLS) between two different complex-valued hyperchaotic systems: Lorenz system and Lü system. By employing Lyapunov stability theory, the active controllers for two synchronization mechanisms are respectively designed to make sure that the synchronization error systems are stabilized at the origin. Moreover, the modified projective lag synchronization between two different complexed hyperchaotic systems is applied to secure communication. Numerical simulations are also given to verify the theoretical results.