| Autor: |
Yuki Hata, Hideaki Matsunaga |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Opuscula Mathematica, Vol 42, Iss 5, Pp 673-690 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
1232-9274 |
| DOI: |
10.7494/OpMath.2022.42.5.673 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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