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| Analysis of Complex Basins of Attraction for Infinite Many Coexisting Steady States in a Class of Rotating Pendulums |
| BAI Ju1, ZHANG Yongxiang1,2, DU Chuanbin2, LIN Mei3
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1. College of Mathematics and Statistics, Qingdao University, Qingdao 266071, China;
2. School of Mathematical Sciences, University of Jinan, Ji’nan 250022, China;
3. Air Force Engineering University, Xi′an 710038, China |
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Abstract For a type of rotating pendulum supported by a spring, it was found that the system has infinite coexisting steady states (attractors), which displays periodic distribution in the phase plane. If at least three connected basins share the same boundary in the phase plane, it is called a complex Wada basin topological boundary. It was found that the basins of the infinitely stable states of the rotating pendulum have Wada basin topological boundaries, and the infinite many basins all have generalized basin cell geometric structure. The complex Wada basin boundary characteristics presented by the rotating pendulum can easily lead to the unpredictability of the final state of the system within the characteristic parameter range and the extremely sensitive dependence of the motion state on the initial conditions. The research results further enrich the dynamics of the rotating pendulum system.
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Received: 13 May 2024
Published: 19 May 2026
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