Periodic second-order systems and coupled forced Van der Pol oscillators
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913191752105984 |
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| author | Minhós, Feliz Perestrelo, Sara |
| author_facet | Minhós, Feliz Perestrelo, Sara |
| contents | We present an existence and localization result for periodic solutions of second-order non-linear coupled planar systems, without requiring periodicity for the non-linearities. The arguments for the existence tool are based on a variation of the Nagumo condition and the Topological Degree Theory. The localization tool is based on a technique of orderless upper and lower solutions, that involves functions with translations. We apply our result to a system of two coupled Van der Pol oscillators with a forcing component. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05387 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Periodic second-order systems and coupled forced Van der Pol oscillators Minhós, Feliz Perestrelo, Sara Dynamical Systems Classical Analysis and ODEs 34A34, 34A12, 34C25, 34C15 We present an existence and localization result for periodic solutions of second-order non-linear coupled planar systems, without requiring periodicity for the non-linearities. The arguments for the existence tool are based on a variation of the Nagumo condition and the Topological Degree Theory. The localization tool is based on a technique of orderless upper and lower solutions, that involves functions with translations. We apply our result to a system of two coupled Van der Pol oscillators with a forcing component. |
| title | Periodic second-order systems and coupled forced Van der Pol oscillators |
| topic | Dynamical Systems Classical Analysis and ODEs 34A34, 34A12, 34C25, 34C15 |
| url | https://arxiv.org/abs/2401.05387 |