@Article{Hata2022,
author = "Hata, Yuki and Matsunaga, Hideaki",
title = "Stability switches in a linear differential equation with two delays",
journal = "Opuscula Math.",
year = "2022",
volume = "42",
number = "5",
pages = "673--690",
doi = "https://doi.org/10.7494/OpMath.2022.42.5.673",
url = "https://doi.org/10.7494/OpMath.2022.42.5.673",
abstract = "This paper is devoted to the study of the effect of delays on the asymptotic stability of a linear differential equation with two delays \[x'(t)=-ax(t)-bx(t-\tau)-cx(t-2\tau),\quad t\geq 0,\] where \(a\), \(b\), and \(c\) are real numbers and \(\tau\gt 0\). We establish some explicit conditions for the zero solution of the equation to be asymptotically stable. As a corollary, it is shown that the zero solution becomes unstable eventually after undergoing stability switches finite times when \(\tau\) increases only if \(c-a\lt 0\) and \(\sqrt{-8c(c-a)}\lt |b| \lt a+c\). The explicit stability dependence on the changing \(\tau\) is also described.",
keywords = "delay differential equations, stability switches, two delays",
issn = "1232-9274"
}