Torus and Subharmonic Motions of a Forced Vibration System in 1: 5 Weak Resonance

Yong Guo

Advances in Mathematical Physics, 2020, vol. 2020, 1-9

Abstract:

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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:5017893

DOI: 10.1155/2020/5017893

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