An exact solution for a non-autonomous delay differential equation
Dynamical Systems
2026-02-20 v4 Adaptation and Self-Organizing Systems
Abstract
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.
Cite
@article{arxiv.2411.11402,
title = {An exact solution for a non-autonomous delay differential equation},
author = {Kenta Ohira},
journal= {arXiv preprint arXiv:2411.11402},
year = {2026}
}
Comments
16 pages, 8 figures, shorter version submitted for publication; ver.2. Fixed some technical errors; ver.3. Fixed some technical errors; ver.4 Fixed some technical erros, adding more references