Explicit Periodic Solutions in a Delay Differential Equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929242013433856 |
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| author | Ivanov, Anatoli Shelyag, Sergiy |
| author_facet | Ivanov, Anatoli Shelyag, Sergiy |
| contents | We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known idea of reduction to interval maps is used in the case under consideration, when both the defining nonlinearity and the periodic coefficient are piece-wise constant functions. The stable periodic dynamics persist under a smoothing procedure in a small neighborhood of the discontinuity set. This work continues the research in recent paper [7] on stable periodic solutions of differential delay equations with periodic coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08197 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit Periodic Solutions in a Delay Differential Equation Ivanov, Anatoli Shelyag, Sergiy Dynamical Systems We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known idea of reduction to interval maps is used in the case under consideration, when both the defining nonlinearity and the periodic coefficient are piece-wise constant functions. The stable periodic dynamics persist under a smoothing procedure in a small neighborhood of the discontinuity set. This work continues the research in recent paper [7] on stable periodic solutions of differential delay equations with periodic coefficients. |
| title | Explicit Periodic Solutions in a Delay Differential Equation |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2402.08197 |