The Neimark-Sacker bifurcation of a forced vibration system is considered in this paper. The series solution to the motion equation is obtained, and the Poincaré map is established. The fixed point of the Poincaré map is guaranteed by the implicit function theorem. The map is transformed into its normal form at the fifth-order resonance case. For some parameter values, there exists the torus . Furthermore, the phenomenon of phase locking on the torus is investigated and the parameter condition under which there exists subharmonic motion on the torus is determined.

中文翻译：

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1：5弱共振的强迫振动系统的圆环和次谐波运动

本文考虑了强制振动系统的Neimark-Sacker分叉。获得了运动方程的级数解，并建立了庞加莱图。隐函数定理可保证庞加莱图的不动点。该图在五阶共振情况下转换为其正常形式。对于某些参数值，存在圆环。此外，研究了在圆环上的锁相现象，并确定了在圆环上存在亚谐波运动的参数条件。