Complete synchronization of chaotic complex nonlinear systems with uncertain parameters

Abstract

Our main objective in this work is to investigate complete synchronization (CS) of n-dimensional chaotic complex systems with uncertain parameters. An adaptive control scheme is designed to study the synchronization of chaotic attractors of these systems. We applied this scheme, as an example, to study complete synchronization of chaotic attractors of two identical complex Lorenz systems. The adaptive control functions and the parameters estimation laws are calculated analytically based on the complex Lyapunov function. We show that the error dynamical systems are globally stable. Numerical simulations are computed to check the analytical expressions of adaptive controllers.

Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System

“…In practical applications, it has always been known that the less the control signal is, the more easily the hardware circuit of the control process is realized. Therefore, the active control synchronization method is easier to be realized in the hardware circuits because of its less control signal and lower cost compared with other control methods [20][21][22]. By the use of this control method in chaotic secure communication, the number of signals transmitted through the public channel can be greatly decreased to further guarantee the security and good robustness.…”

“…In recent years, Mahmoud et al introduced some chaotic and hyperchaotic systems with complex variables, analyzed their chaotic behavior, and proposed several types of synchronization methods [20][21][22][23][24][25]. Usually, increasingly novel chaotic systems are generated from low-order chaotic systems to hyperchaotic systems [26][27][28] and from two-wing systems to four-wing or multiloop systems [29][30][31][32].…”

Design and analysis on Synchronization of a Fractional-order Bloch System

“…It is well known that synchronization was proposed in 1990 [6]. Nowadays, synchronization of integer-order systems has been studied extensively and several methods are extended to synchronize fractional-order systems [7][8][9].…”

Switched modified function projective synchronization between two complex nonlinear hyperchaotic systems based on adaptive control and parameter identification

“…[9] introduced a complex Lorenz model to generalize the real Lorenz model in 1982, complex chaotic and hyperchaotic systems have attracted increasing attention due to the fact that the systems with complex variables can be used to describe the physics of a detuned laser, rotating fluids, disk dynamos, electronic circuits, and particle beam dynamics in high energy accelerators [17]. When applying the complex systems in communications, the complex variables will double the number of variables and can increase the content and security of the transmitted information.…”