Modulus Synchronization of a Novel Hyperchaotic Real System and Its Corresponding Complex System

The synchronization of chaotic real systems or chaotic complex systems has been extensively discussed in previously conducted studies. However, much is not known regarding the synchronization between complex drive systems and real response systems. This study investigates a novel modulus synchronization between a hyperchaotic real system and its corresponding complex system. The systems are designed and their dynamical properties including invariance, dissipation, equilibria, Lyapunov exponents and the spectrum of them, as well as hyperchaotic attractors are analyzed in detail. Moreover, the adaptive controller is also developed based on Lyapunov stability theory. Furthermore, the numerical simulation experiments verify the effectiveness of our idea.