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Distributional Chaos and Sensitivity for a Class of Cyclic Permutation Maps

Author

Listed:
  • Yu Zhao

    (School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China)

  • Waseem Anwar

    (Department of Mathematics, Sichuan Normal University, Chengdu 610017, China)

  • Risong Li

    (School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China
    ArtificialIntelligence Key Laboratory, Bridge Non-Destruction Detecting and Engineering Computing Key Laboratory of Sichuan Province, Zigong 643000, China)

  • Tianxiu Lu

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

  • Zhiwen Mo

    (Department of Mathematics, Sichuan Normal University, Chengdu 610017, China)

Abstract

Several chaotic properties of cyclic permutation maps are considered. Cyclic permutation maps refer to p -dimensional dynamical systems of the form φ ( b 1 , b 2 , ⋯ , b p ) = ( u p ( b p ) , u 1 ( b 1 ) , ⋯ , u p − 1 ( b p − 1 ) ) , where b j ∈ H j ( j ∈ { 1 , 2 , ⋯ , p } ), p ≥ 2 is an integer, and H j ( j ∈ { 1 , 2 , ⋯ , p } ) are compact subintervals of the real line R = ( − ∞ , + ∞ ) . u j : H j → H j + 1 ( j = 1 , 2 , … , p − 1 ) and u p : H p → H 1 are continuous maps. Necessary and sufficient conditions for a class of cyclic permutation maps to have Li–Yorke chaos, distributional chaos in a sequence, distributional chaos, or Li–Yorke sensitivity are given. These results extend the existing ones.

Suggested Citation

  • Yu Zhao & Waseem Anwar & Risong Li & Tianxiu Lu & Zhiwen Mo, 2023. "Distributional Chaos and Sensitivity for a Class of Cyclic Permutation Maps," Mathematics, MDPI, vol. 11(15), pages 1-9, July.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3310-:d:1204453
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    References listed on IDEAS

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