Speaker
Description
Delays in feedback mechanisms are well known to generate complex behavior, including oscillations. Understanding delay effects is therefore important in fields such as biology, mathematics, economics, and engineering. Delay differential equations (DDEs) provide a natural framework for analyzing such systems, yet exact analytical solutions are rare.
We present an exact solution of a simple non-autonomous DDE, which to our knowledge is the first analytical result of this type. Using this solution, we study a coupled system of two such equations. For suitable parameter values, the oscillation amplitude is dramatically enhanced - up to about 10 to the 8 times larger than in the uncoupled case.
Large collective oscillations are often assumed to require many interacting units. For example, the sinoatrial node, the heart’s primary pacemaker, contains thousands to tens of thousands of cells. Our results indicate that the presence of delay can produce strong amplification even in systems with only a small number of units.
Bibliography
@article{Ohira2025SIADS,
author = {Ohira, Kenta},
title = {An Exact Solution for a Nonautonomous Delay Differential Equation},
journal = {SIAM Journal on Applied Dynamical Systems},
volume = {24},
number = {4},
pages = {3169--3182},
year = {2025},
month = dec,
doi = {10.1137/25M1738164}
}
@article{Ohira2025Chaos,
author = {Ohira, Kenta and Ohira, Toru and Ohira, Hideki},
title = {Amplitude Enhancements through Rewiring of a Non-Autonomous Delay System},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
volume = {35},
number = {4},
pages = {041101},
year = {2025},
doi = {10.1063/5.0252300},
publisher = {AIP Publishing}
}
