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

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  • Jiezhi Wang
  • Qing Zhang
  • Zengqiang Chen
  • Hang Li

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 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.

Suggested Citation

  • Jiezhi Wang & Qing Zhang & Zengqiang Chen & Hang Li, 2014. "Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, July.
    • Handle: RePEc:hin:jnlaaa:781594
    DOI: 10.1155/2014/781594
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    Cited by:

    1. Ren, Lei & Lin, Ming-Hung & Abdulwahab, Abdulkareem & Ma, Jun & Saberi-Nik, Hassan, 2023. "Global dynamical analysis of the integer and fractional 4D hyperchaotic Rabinovich system," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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