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Mathematical Problems in Engineering
Volume 2013, Article ID 179428, 8 pages
Research Article

A New Four-Dimensional Autonomous Hyperchaotic System and the Synchronization of Different Chaotic Systems by Using Fast Terminal Sliding Mode Control

1Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China
2School of Mathematics and Information Science, Qujing Normal University, Qujing 655011, China

Received 24 September 2013; Revised 28 November 2013; Accepted 28 November 2013

Academic Editor: Tomasz Kapitaniak

Copyright © 2013 Baojie Zhang and Hongxing Li. 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 presents a new continuous-time four-dimensional autonomous system based on Lorenz system. We analyze the dissipation, equilibrium, and Lyapunov exponents of the system. Lyapunov exponent spectrum demonstrates that the system possesses rich dynamic behaviors if the parameters of the system vary. In a large range of parameters, the system is hyperchaotic. By using fast terminal sliding mode control method, the synchronization of two different chaotic systems is studied. Synchronization between the new system and hyperchaotic Chen system with noise perturbation is illustrated. Simulation results verify the effectiveness of the proposed method.