Asymmetric Duffing oscillator: metamorphoses of $1:2$ resonance and its interaction with the primary resonance
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909260451938304 |
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| author | Kyziol, Jan Okniński, Andrzej |
| author_facet | Kyziol, Jan Okniński, Andrzej |
| contents | We investigate the $1: 2$ resonance in the periodically forced asymmetric Duffing oscillator due to the period-doubling of the primary $1: 1$ resonance or forming independently, coexisting with the primary resonance. We compute the steady-state asymptotic solution - the amplitude-frequency implicit function. Working in the differential properties of implicit functions framework, we describe complicated metamorphoses of the $1:2$ resonance and its interaction with the primary resonance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03423 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymmetric Duffing oscillator: metamorphoses of $1:2$ resonance and its interaction with the primary resonance Kyziol, Jan Okniński, Andrzej Chaotic Dynamics 37G35, 37M20 We investigate the $1: 2$ resonance in the periodically forced asymmetric Duffing oscillator due to the period-doubling of the primary $1: 1$ resonance or forming independently, coexisting with the primary resonance. We compute the steady-state asymptotic solution - the amplitude-frequency implicit function. Working in the differential properties of implicit functions framework, we describe complicated metamorphoses of the $1:2$ resonance and its interaction with the primary resonance. |
| title | Asymmetric Duffing oscillator: metamorphoses of $1:2$ resonance and its interaction with the primary resonance |
| topic | Chaotic Dynamics 37G35, 37M20 |
| url | https://arxiv.org/abs/2407.03423 |