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The basin of attraction of the Chen attractor

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  • Liu, Zengrong
  • Li, Ying
  • Chen, Guanrong

Abstract

By geometric analysis, we discuss the riddled property of the basin of attraction of the Chen attractor based on Milnor’s definition, and prove that any neighborhood of the Chen attractor contains repelled sets with positive Lebesque measures. Our analytic and numerical results show that the Chen attractor indeed has some unusual properties leading to a “strange attractor” in the sense of Milnor.

Suggested Citation

  • Liu, Zengrong & Li, Ying & Chen, Guanrong, 2007. "The basin of attraction of the Chen attractor," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1696-1703.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:5:p:1696-1703
    DOI: 10.1016/j.chaos.2006.05.008
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    Cited by:

    1. Zhong, Xiaoyun & Peng, Minfang & Tse, Chi K. & Guo, Shangjiang & Shahidehpour, Mohammad, 2015. "Analysis and control of multiple chaotic attractors from a three-dimensional system," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 138-150.
    2. González, Graciela Adriana & Nielsen, Christopher & Bortoff, Zachary, 2022. "Attractivity of unstable equilibria for a controlled Chen system via small output feedback," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Figueiredo, Annibal & Rocha Filho, Tarcisio M., 2009. "Basins of attraction of invariant regular manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1877-1889.

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