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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 781594, 9 pages
Research Article

Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization

1College of Science, Civil Aviation University of China, Tianjin 300300, China
2Department of Automation, Nankai University, Tianjin 300071, China
3Economics and Management College, Civil Aviation University of China, Tianjin 300300, China

Received 27 March 2014; Accepted 27 June 2014; Published 14 July 2014

Academic Editor: Josef Diblík

Copyright © 2014 Jiezhi Wang 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.


Two ellipsoidal ultimate boundary regions of a special three-dimensional (3D) chaotic system are proposed. To this chaotic system, the linear coefficient of the th state variable in the th state equation has the same sign; it also has two one-order terms and one quadratic cross-product term in each equation. A numerical solution and an analytical expression of the ultimate bounds are received. To get the analytical expression of the ultimate boundary region, a new result of one maximum optimization question is proved. The corresponding ultimate boundary regions are demonstrated through numerical simulations. Utilizing the bounds obtained, a linear controller is proposed to achieve the complete chaos synchronization. Numerical simulation exhibits the feasibility of the designed scheme.