TY  - JOUR
ID  - Hata2022
LB  - Hata2022
AU  - Hata, Yuki
AU  - Matsunaga, Hideaki
TI  - Stability switches in a linear differential equation with two delays
ST  - Stability switches in a linear differential equation with two delays
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2022
VL  - 42
IS  - 5
SP  - 673
EP  - 690
DO  - https://doi.org/10.7494/OpMath.2022.42.5.673
UR  - https://doi.org/10.7494/OpMath.2022.42.5.673
AB  - 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.
KW  - delay differential equations
KW  - stability switches
KW  - two delays
SN  - 1232-9274
ER  -