Generalized complex projective synchronization of chaotic complex systems with unknown parameters

In this paper, we developed a complex projective synchronization for complex chaotic systems. We generalized a complex scaling matrix for synchronizing two chaotic systems with different orders. We proposed an adaptive control method to synchronize between drive and response chaotic complex systems with fully unknown parameters. Based on Lyapunov theorem, we proved the stability of the synchronization. Numerical simulations are given to verify the proposed method.