The discontinuous limit case of an archetypal oscillator with constant excitation and van der Pol damping: A single equilibrium
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908626057166848 |
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| author | Cen, Xiuli Chen, Hebai Tang, Yilei Wang, Zhaoxia |
| author_facet | Cen, Xiuli Chen, Hebai Tang, Yilei Wang, Zhaoxia |
| contents | This paper investigates the global dynamics of the discontinuous limit case of an archetypal oscillator with constant excitation that exhibits a single equilibrium. For parameter regions in which this oscillator possesses two or three equilibria, the global bifurcation diagram and the corresponding phase portraits on the Poincare disc have been presented in [Phys. D, 438 (2022) 133362]. The present work completes the global structure of the discontinuous limit case of an archetypal oscillator with constant excitation. Although the dynamical phenomena are less rich compared to systems with more than one equilibrium, the presence of a single equilibrium gives rise to additional limit cycles surrounding it, thereby enriching the overall dynamics and making the analysis substantially more intricate than in the previously studied cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01922 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The discontinuous limit case of an archetypal oscillator with constant excitation and van der Pol damping: A single equilibrium Cen, Xiuli Chen, Hebai Tang, Yilei Wang, Zhaoxia Dynamical Systems Classical Analysis and ODEs This paper investigates the global dynamics of the discontinuous limit case of an archetypal oscillator with constant excitation that exhibits a single equilibrium. For parameter regions in which this oscillator possesses two or three equilibria, the global bifurcation diagram and the corresponding phase portraits on the Poincare disc have been presented in [Phys. D, 438 (2022) 133362]. The present work completes the global structure of the discontinuous limit case of an archetypal oscillator with constant excitation. Although the dynamical phenomena are less rich compared to systems with more than one equilibrium, the presence of a single equilibrium gives rise to additional limit cycles surrounding it, thereby enriching the overall dynamics and making the analysis substantially more intricate than in the previously studied cases. |
| title | The discontinuous limit case of an archetypal oscillator with constant excitation and van der Pol damping: A single equilibrium |
| topic | Dynamical Systems Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2511.01922 |