Abstract
In this paper, generalized synchronization (GS) is extended from real space to complex space, resulting in a new synchronization scheme, complex generalized synchronization (CGS). Based on Lyapunov stability theory, an adaptive controller and parameter update laws are designed to realize CGS and parameter identification of two nonidentical chaotic (hyperchaotic) complex systems with respect to a given complex map vector. This scheme is applied to synchronize a memristor-based hyperchaotic complex Lü system and a memristor-based chaotic complex Lorenz system, a chaotic complex Chen system and a memristor-based chaotic complex Lorenz system, as well as a memristor-based hyperchaotic complex Lü system and a chaotic complex Lü system with fully unknown parameters. The corresponding numerical simulations illustrate the feasibility and effectiveness of the proposed scheme.
Highlights
Since Fowler et al proposed a complex Lorenz system in 1982 [1], modeling, analyses and synchronization of complex systems have attracted more and more attention in nonlinear science and technology fields, the reasons of which can be roughly summed up in the following two aspects
Some physical systems and phenomena should be accurately modeled by complex systems, such as rotating fluids, detuned lasers, disk dynamos, electronic circuits, and so on [1,2,3,4]; on the other, due to the existence of complex variables which can double the number of variables, complex systems can generate complicated dynamical behaviors with strong unpredictability, and synchronization of complex systems has widely potential applications to many fields of physics, ecological systems, signal and information processing, and system identification, especially to secure communication for achieving higher transmission efficiency and anti-attack ability [5,6,7]
Chaos synchronization is the precondition of chaotic secure communication, digital cryptography, chaotic image encryption, etc
Summary
Since Fowler et al proposed a complex Lorenz system in 1982 [1], modeling, analyses and synchronization of complex systems have attracted more and more attention in nonlinear science and technology fields, the reasons of which can be roughly summed up in the following two aspects. Zhang et al investigated the complex modified projective synchronization (CMPS) and parameter identification of uncertain real chaotic systems and complex chaotic systems [20]. Liu et al used an adaptive complex modified projective synchronization (ACMPS) method to synchronize two chaotic (hyperchaotic) complex systems up to a complex scaling matrix, and to estimate the unknown complex parameters successfully [21]. It is meaningful and challenging to extend GS from real systems to complex systems, and to realize CGS and parameter identification of chaotic and hyperchaotic complex systems with unknown parameters. Motivated by the above discussions, this paper investigates CGS and parameter identification of different chaotic and hyperchaotic complex systems with unknown parameters.
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