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Journal of Control Science and Engineering
Volume 2018, Article ID 5603639, 5 pages
Research Article

Hybrid Synchronization of Uncertain Generalized Lorenz System by Adaptive Control

Department of Mathematics and Finance, Hanjiang Normal University, Hubei 442000, China

Correspondence should be addressed to Xinlian Zhou; moc.qq@600449355 and Yuhua Xu; moc.361@4002uxauhuy

Received 28 October 2017; Revised 18 December 2017; Accepted 19 December 2017; Published 24 January 2018

Academic Editor: Sundarapandian Vaidyanathan

Copyright © 2018 Xinlian Zhou and Yuhua Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.