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Abstract and Applied Analysis
Volume 2013, Article ID 415652, 12 pages
Research Article

Reduced-Order Antisynchronization of Chaotic Systems via Adaptive Sliding Mode Control

1School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
2Mathematics Department, Faculty of Science, University of Hail, Hail 81451, Saudi Arabia

Received 10 May 2013; Accepted 26 August 2013

Academic Editor: Juan Carlos Cortés López

Copyright © 2013 Wafaa Jawaada et al. 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.


A novel reduced-order adaptive sliding mode controller is developed and experimented in this paper to antisynchronize two different chaotic systems with different order. Based upon the parameters modulation and the adaptive sliding mode control techniques, we show that dynamical evolution of third-order chaotic system can be antisynchronized with the projection of a fourth-order chaotic system even though their parameters are unknown. The techniques are successfully applied to two examples: firstly Lorenz (4th-order) and Lorenz (3rd-order) and secondly the hyperchaotic Lü (4th-order) and Chen (3rd-order). Theoretical analysis and numerical simulations are shown to verify the results.