Stability switches in a linear differential equation with two delays

• Autorzy: Hata Yuki , Matsunaga Hideaki

Identyfikatory

DOI

10.7494/OpMath.2022.42.5.673

• Języki publikacji: EN

Abstrakty

EN

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 − τ ) − cx(t − 2τ ), t ≥ 0, where a, b, and c are real numbers and τ > 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 τ increases only if c−a < 0 and [formula]. The explicit stability dependence on the changing τ is also described.

Słowa kluczowe

EN

delay differential equations; stability switches; two delays

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2022
• Tom: Vol. 42, no. 5
• Strony: 673--690
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Hata Yuki

• Osaka Prefecture University, Department of Mathematical Sciences, Sakai 599-8531, Japan

autor

Matsunaga Hideaki

• Osaka Metropolitan University, Department of Mathematics, Sakai 599-8531, Japan

• https://orcid.org/0000-0001-5805-2303

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).