Delayed Dynamics with Transient Resonating Oscillations
Abstract
Recently, we have studied a delay differential equation which has a coefficient that is a linear function of time. The equation has shown the oscillatory transient dynamics appear and disappear as the delay is increased between zero to asymptotically large delay. We here propose and study another equation that shows similar transient oscillations. It has an extra exponential gaussian factor on the delayed feedback term. It is shown that this equation is analytically tractable with the use of the Lambert function. This equation is also studied numerically to confirm some of the properties inferred from the analytical solution. We also have found that the amplitude of transient oscillation changes and goes through a maximum as we increase the value of the delay. In this sense, the proposed equation is one of the simplest dynamical equations that brings out a resonant behavior without any external oscillating inputs.
Cite
@article{arxiv.2201.12058,
title = {Delayed Dynamics with Transient Resonating Oscillations},
author = {Kenta Ohira and Toru Ohira},
journal= {arXiv preprint arXiv:2201.12058},
year = {2023}
}
Comments
18 pages, 7 figures, version 2: Some typos and errors fixed; version 3: An author and reference added, and errors fixed; version 4: extensively revised final published version; Version 5: Corrected some technical errors and updated figures and tables accordingly from the published version