Lag Synchronization of Complex Lorenz System with Applications to Communication

Abstract

In communication, the signal at the receiver end at time t is the signal from the transmitter side at time t − τ (τ ≥ 0 and it is the lag time) as the time lag of transmission. Therefore, lag synchronization (LS) is more accurate than complete synchronization to design communication scheme. Taking complex Lorenz system as an example, we design the LS controller according to error feedback. Using chaotic masking, we propose a communication scheme based on LS and independent component analysis (ICA). It is suitable to transmit multiple messages with all kinds of amplitudes and it has the ability of anti-noise. Numerical simulations verify the feasibility and effectiveness of the presented schemes.

Simplified method and synchronization for a class of complex chaotic systems

“…[2][3][4] Over the past three decades, the research on dynamic and synchronization control of real chaotic systems had been attracting a great deal of attention, [5][6][7][8][9] but the study of complex chaotic systems was not too much. For complex chaotic systems, the complex variable increases the amount of information in secure communication and enhances the security of communication, [10][11][12][13][14] so it has great research value.…”

“…So the error system(14) can be rewritten as below _ e x = σ e y − e x À Á _ e y = −x i e z −ae y _ e z = − be z + 1 + k 2…”

Complex Generalized Synchronization and Parameter Identification of Nonidentical Nonlinear Complex Systems

“…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. On the one hand, 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 – 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 – 7 ].…”

A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

“…[22][23][24][25][26][27][28][29], and it has been a popular research area. Recently, a number of control schemes have been developed to achieve various synchronization of memristor-based systems and complex systems.…”

“…The adopted synchronization schemes include adaptive control [30][31][32], backstepping control [33], fuzzy control [8], impulsive control [34,35], etc. The realized synchronization types include complete synchronization [36,37], anti-synchronization [32], projective synchronization [23,38], lag synchronization [24,39], combination synchronization [40,41], compound synchronization [10], etc. However, to our best knowledge, memristor-based complex systems are not involved in the existing literature, unfortunately.…”