GENERALIZED SYNCHRONIZATION AND PARAMETERS IDENTIFICATION OF DIFFERENT-DIMENSIONAL CHAOTIC SYSTEMS IN THE COMPLEX FIELD

Abstract

Generalized synchronization is a typical dynamical phenomenon in nonlinear systems, for which the real-valued setting has been widely investigated. The complex-valued functions relationship in generalized synchronization is equally important for complex-valued dynamical systems, which however are seldom studied. Complex parameters identification on the synchronization manifold remains an open problem owing to the absence of the persistent excitation (PE) condition in the complex field. This paper investigates generalized synchronization via a complex-valued vector mapping (CGS) for different-dimensional complex-variable chaotic (hyper-chaotic) systems (CVCSs) with complex parameters identification. Based on Lyapunov stability theory in the complex field and using an adaptive control method, some sufficient criteria are established to achieve CGS for CVCSs. Moreover, some necessary and sufficient criteria are derived to ensure complex parameters identification. Finally, the theoretical results are verified and demonstrated by reduced-order and increased-order simulation examples.