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Wang, Jiezhi; Zhang, Qing; Chen, Zengqiang; Li, Hang

Ultimate bound of a 3D chaotic system and its application in chaos synchronization. (English) Zbl 1406.93137

Abstr. Appl. Anal. 2014, Article ID 781594, 9 p. (2014).
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 \(i\)th state variable in the \(i\)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.

Cited in 1 Document

MSC:

93C05 Linear systems in control theory
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Keywords:

3D chaotic system; chaos synchronization; ultimate boundary region; linear controller
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References:

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