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

Two ellipsoidal ultimate boundary regions of a special three-dimensional (3D) chaotic system are proposed. To this chaotic system, the linear coefficient of the ith state variable in the ith state equation has the same sign; it also has two one-order terms and one quadratic cross-product term in eac...

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Bibliographic Details
Main Authors: Jiezhi Wang, Qing Zhang, Zengqiang Chen, Hang Li
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/781594
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Summary:Two ellipsoidal ultimate boundary regions of a special three-dimensional (3D) chaotic system are proposed. To this chaotic system, the linear coefficient of the ith state variable in the ith 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.
ISSN:1085-3375
1687-0409