On the formation of the 1:2 resonance in oscillator dynamics
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918284957319168 |
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| author | Kyzioł, Jan Okniński, Andrzej |
| author_facet | Kyzioł, Jan Okniński, Andrzej |
| contents | The dynamics of nonlinear oscillators are investigated. We study the formation of $1:2$ resonance in nonlinear periodically forced oscillators due to period doubling of the primary $1:1$ resonance, or born independently. We compute the amplitude-frequency implicit function, the steady-state asymptotic solution, for the effective equation approximating coupled oscillators. Working in the framework of differential properties of implicit functions, we demonstrate that birth of $1:2$ resonances corresponds to singular isolated points of the implicit functions. We provide numerical examples illustrating our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13394 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the formation of the 1:2 resonance in oscillator dynamics Kyzioł, Jan Okniński, Andrzej Chaotic Dynamics 34C05, 34C15, 37M20, 70K30 The dynamics of nonlinear oscillators are investigated. We study the formation of $1:2$ resonance in nonlinear periodically forced oscillators due to period doubling of the primary $1:1$ resonance, or born independently. We compute the amplitude-frequency implicit function, the steady-state asymptotic solution, for the effective equation approximating coupled oscillators. Working in the framework of differential properties of implicit functions, we demonstrate that birth of $1:2$ resonances corresponds to singular isolated points of the implicit functions. We provide numerical examples illustrating our theoretical findings. |
| title | On the formation of the 1:2 resonance in oscillator dynamics |
| topic | Chaotic Dynamics 34C05, 34C15, 37M20, 70K30 |
| url | https://arxiv.org/abs/2503.13394 |