Abstract: For an elastically supported rotor-stator rubbing system, the dynamic response was numerically solved using a variable-step Runge-Kutta method. The continuation algorithm was integrated with the shooting method to trace the evolutionary paths of coexisting periodic solutions, systematically analyzing their stability and bifurcation behavior. By examining the basin topology, phase trajectories, and Poincaré sections, the erosion dynamics of coexisting attractors’ basins under parametric perturbations were elucidated. The results demonstrate that variations in rotational speed induce grazing-induced saddle-node bifurcations, jump bifurcations, and period-doubling bifurcations, leading to multistability (coexistence of multiple attractors) accompanied by symmetric motion patterns. Saddle-node bifurcations trigger abrupt topological restructuring of basins, whereas period-doubling bifurcations exhibit negligible influence on basin morphology. These findings provide a theoretical foundation for optimizing system operation across diverse rotational speeds and establish a theoretical basis for stabilizing control of rotor-stator rubbing systems.

摘要： 针对弹性支撑碰摩转子系统，通过变步长Runge-Kutta 法数值求解系统动力学响应，并融合延拓算法与打靶法追踪共存周期解的演化路径，系统分析其稳定性与分岔行为。结合吸引域拓扑、相轨迹及Poincaré 截面，阐明参数扰动下共存吸引子的域侵蚀机制。研究发现：转速变化诱发擦边-鞍结分岔、跳跃分岔及倍周期分岔时，系统呈现多吸引子共存现象，且伴随对称性运动模式。鞍结分岔会导致其吸引域的拓扑结构发生突变，而倍周期分岔对其吸引域的影响较小。该研究成果可为不同转速工况下的系统运行优化提供理论支撑，为碰摩转子系统的稳定控制提供理论依据。

关键词: 振动与波, 碰摩, 转子系统, 打靶法, 共存吸引子, 稳定性, 吸引域