Abstract
This paper investigates hybrid synchronization of the uncertain generalized Lorenz system. Several useful criteria are given for synchronization of two generalized Lorenz systems, and the adaptive control law and the parameter update law are used. In comparison with those of existing synchronization methods, hybrid synchronization includes full-order synchronization, reduced-order synchronization, and modified projective synchronization. What is more, control of the stability point, complete synchronization, and antisynchronization can coexist in the same system. Numerical simulations show the effectiveness of this method in a class of chaotic systems.
Highlights
In 1990, Pecora and Carroll made chaos synchronization come true [1]; chaotic synchronization, as a very important topic in the nonlinear science, has been extensively studied in a variety of fields including secure communications and physical and biological systems [2, 3]
A lot of methods about chaotic synchronization have been presented to prove that the chaotic synchronization method is feasible, such as linear and nonlinear feedback synchronization [4, 5], impulsive synchronization [6], adaptive synchronization [7], and observer based control method [8]
Hybrid synchronization is one in which some of the chaotic systems are synchronized whereas others are antisynchronized [9]
Summary
In 1990, Pecora and Carroll made chaos synchronization come true [1]; chaotic synchronization, as a very important topic in the nonlinear science, has been extensively studied in a variety of fields including secure communications and physical and biological systems [2, 3]. A lot of methods about chaotic synchronization have been presented to prove that the chaotic synchronization method is feasible, such as linear and nonlinear feedback synchronization [4, 5], impulsive synchronization [6], adaptive synchronization [7], and observer based control method [8] Among these schemes, hybrid synchronization is one in which some of the chaotic systems are synchronized whereas others are antisynchronized [9]. Based on the stability theory of systems, several useful criteria are given for discussing synchronization of two generalized Lorenz systems, and the adaptive control law and the parameter update law are given. In comparison with those of existing synchronization methods, hybrid synchronization includes full-order synchronization, reduced-order synchronization, and the modified projective synchronization.
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