Full State Hybrid Projective Synchronization and Parameters Identification for Uncertain Chaotic (Hyperchaotic) Complex Systems

Abstract

We introduce the definition of full state hybrid projective synchronization (FSHPS) with complex scaling factors for chaotic and hyperchaotic complex systems and design adaptive FSHPS schemes for uncertain chaotic complex systems under bounded disturbances with all possible situations of unknown parameters. The proposed schemes guarantee adaptive FSHPS between two chaotic complex systems with a small error bound and the convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Then we draw on the sufficient condition and necessary condition that the unknown parameters converge to their true values based on the persistency of excitation (PE) and linear independence (LI). At last, we realize adaptive FSHPS between uncertain complex Chen and Lü systems, which verify the feasibility and effectiveness of the presented schemes.