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Mathematical Problems in Engineering
Volume 2015, Article ID 434651, 7 pages
Research Article

Synchronization and Antisynchronization for a Class of Chaotic Systems by a Simple Adaptive Controller

School of Science, Qilu University of Technology, Jinan 250353, China

Received 21 August 2015; Accepted 20 October 2015

Academic Editor: Jonathan N. Blakely

Copyright © 2015 Ling Ren and Rongwei Guo. 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 the synchronization and antisynchronization for a class of chaotic system. Firstly, a necessary and sufficient condition is proposed to synchronize and antisynchronization simultaneously for the chaotic systems. Secondly, two methods are obtained to realize coexistence of synchronization and antisynchronization in the chaotic systems, and the corresponding adaptive controllers are also given. Finally, two numerical examples with simulation verify the correctness and effectiveness of the obtained results.