General hybrid projective complete dislocated synchronization between a class of chaotic real nonlinear systems and a class of chaotic complex nonlinear systems

The synchronization of a class of chaotic real nonlinear systems and the synchronization of a class of chaotic complex nonlinear systems have been widely reported in the previous studies, respectively. In the paper, we investigate the general hybrid projective complete dislocated synchronization between a class of chaotic real nonlinear systems and a class of chaotic complex nonlinear systems for the first time. Based on the Lyapunov stability theory, an feedback control scheme has been designed to realize the general hybrid projective complete dislocated synchronization between a class of chaotic real nonlinear systems and a class of chaotic complex nonlinear systems with different initial conditions. The general hybrid projective complete dislocated synchronization between the real Lorenz system and the complex Lorenz system, the hyperchaotic real Lü system and the hyperchaotic complex Lü system are presented as two examples to demonstrate the validity and feasibility of the presented idea.