WADA BASINS IN AN UNCONTROLLED AND CONTROLLED VIBRATION ISOLATION SYSTEM

Yongxiang Zhang and Fanhui Zhang
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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

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-12

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.

Keywords: Basin of Attraction; Fractal Basin Boundary; Wada Basin; Fractal Attractors (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500049

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