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

Jiezhi Wang, Qing Zhang, Zengqiang Chen and Hang Li

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: 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.

Date: 2014
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https://doi.org/10.1155/2014/781594

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:781594

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