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Wada Basins In An Uncontrolled And Controlled Vibration Isolation System

Author

Listed:
  • YONGXIANG ZHANG

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, P. R. China)

  • FANHUI ZHANG

    (School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P. R. China)

Abstract

It is an open question whether Wada basin exists in control systems. We investigate coexisting attractors and their Wada basins for a given set of parameters in an uncontrolled and controlled vibration isolation system. Wada basins are verified by the Nusse–Yorke method. All coexisting chaotic attractors can be converted into periodic attractors but the basin structure can still possess Wada property by two control methods (an external drive control and a piecewise damping control) with the appropriate control parameters. The Wada basins of controlled systems imply a particular kind of unpredictability, and we should avoid selecting such control parameters although chaotic attractors are effectively controlled.

Suggested Citation

  • Yongxiang Zhang & Fanhui Zhang, 2022. "Wada Basins In An Uncontrolled And Controlled Vibration Isolation System," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-12, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22500049
    DOI: 10.1142/S0218348X22500049
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