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Stability and Bifurcation Analysis of Coexisting Attractors for Bumper Rotor Systems
2026, 46(5):
22-28.
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.
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