针对一类由弹簧支撑的旋转摆,发现系统存在无穷多共存稳态(吸引子),这些共存稳态在相平面内呈周期性分布。若相平面内至少3个连通的吸引域共享相同的边界称为复杂Wada域拓扑边界,研究发现该旋转摆无穷多稳态的吸引域都具有Wada域拓扑边界,无穷多吸引域都具有广义域胞几何结构。旋转摆呈现出的复杂Wada域边界特性,容易导致系统在特性参数范围内终态的不可预测性以及运动状态对初始条件的极度敏感依赖性。研究结果进一步丰富了旋转摆系统的动力学。
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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