Various methods for modified projective synchronization of Liu system and the new Lorenz system

In this paper, we mainly concern the synchronization of Liu hyperchaotic system and the new Lorenz hyperchaotic system. Within the two systems, we achieve the modified projective synchronization (MPS) and adaptive modified projective synchronization (AMPS). In addition, based on the Lyapunov stability theory, the adaptive modified projective dislocated synchronization (AMPDS) is proposed, which realizes the projective dislocated synchronization between two systems with uncertain parameters. Numerical examples are given to show the feasibility and effectiveness of these methods.