An exact solution for a non-autonomous delay differential equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915804793012224 |
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| author | Ohira, Kenta |
| author_facet | Ohira, Kenta |
| contents | We derive an exact solution for a simple non-autonomous delay differential equation (DDE) over the entire real-time axis, representing it as a sum of Gaussian-shaped dynamics with distinct peak positions. This marks the first explicit solution for non-autonomous DDEs and is a rare example even among general DDEs. The constructed solution offers key physical insights and facilitates the analysis of system properties, such as the envelope profile of the dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11402 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An exact solution for a non-autonomous delay differential equation Ohira, Kenta Dynamical Systems Adaptation and Self-Organizing Systems We derive an exact solution for a simple non-autonomous delay differential equation (DDE) over the entire real-time axis, representing it as a sum of Gaussian-shaped dynamics with distinct peak positions. This marks the first explicit solution for non-autonomous DDEs and is a rare example even among general DDEs. The constructed solution offers key physical insights and facilitates the analysis of system properties, such as the envelope profile of the dynamics. |
| title | An exact solution for a non-autonomous delay differential equation |
| topic | Dynamical Systems Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2411.11402 |