Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak Resonance
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 no...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/5017893 |
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| author | Yong Guo |
| author_facet | Yong Guo |
| author_sort | Yong Guo |
| collection | DOAJ |
| description | 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 T1. Furthermore, the phenomenon of phase locking on the torus T1 is investigated and the parameter condition under which there exists subharmonic motion on the torus T1 is determined. |
| format | Article |
| id | doaj-art-cbbded71025b42ec947b0126bca6f16f |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-cbbded71025b42ec947b0126bca6f16f2025-02-03T01:28:16ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/50178935017893Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak ResonanceYong Guo0School of Civil Engineering, Guizhou Institute of Technology, Guiyang, ChinaThe 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 T1. Furthermore, the phenomenon of phase locking on the torus T1 is investigated and the parameter condition under which there exists subharmonic motion on the torus T1 is determined.http://dx.doi.org/10.1155/2020/5017893 |
| spellingShingle | Yong Guo Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak Resonance Advances in Mathematical Physics |
| title | Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak Resonance |
| title_full | Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak Resonance |
| title_fullStr | Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak Resonance |
| title_full_unstemmed | Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak Resonance |
| title_short | Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak Resonance |
| title_sort | torus and subharmonic motions of a forced vibration system in 1 5 weak resonance |
| url | http://dx.doi.org/10.1155/2020/5017893 |
| work_keys_str_mv | AT yongguo torusandsubharmonicmotionsofaforcedvibrationsystemin15weakresonance |