Hybrid dislocated control and general hybrid projective dislocated synchronization for the modified Lü chaotic system

Abstract

This paper introduces a modified Lü chaotic system, and some basic dynamical properties are studied. Based on these properties, we present hybrid dislocated control method for stabilizing chaos to unstable equilibrium and limit cycle. In addition, based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization (GHPDS) is proposed, which includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. The drive and response systems discussed in this paper can be strictly different dynamical systems (including different dimensional systems). As examples, the modified Lü chaotic system, Chen chaotic system and hyperchaotic Chen system are discussed. Numerical simulations are given to show the effectiveness of these methods.