Regions of Stability for a Linear Differential Equation with Two Rationally Dependent Delays
Dynamical Systems
2013-08-08 v1
Abstract
Stability analysis is performed for a linear differential equation with two delays. Geometric arguments show that when the two delays are rationally dependent, then the region of stability increases. When the ratio has the form 1/n, this study finds the asymptotic shape and size of the stability region. For example, a delay ration of 1/3 asymptotically produces a stability region 44.3% larger than any nearby delay ratios, showing extreme sensitivity in the delays. The study provides a systematic and geometric approach to finding the eigenvalues on the boundary of stability for this delay differential equation. A nonlinear model with two delays illustrates how our methods can be applied.
Keywords
Cite
@article{arxiv.1308.1427,
title = {Regions of Stability for a Linear Differential Equation with Two Rationally Dependent Delays},
author = {Joseph M. Mahaffy and Timothy C. Busken},
journal= {arXiv preprint arXiv:1308.1427},
year = {2013}
}