Address: Department of Mathematics, Osaka Metropolitan University, Sakai 599-8531, Japan
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Abstract: This paper is devoted to the investigation on the stability for two characteristic functions $f_1(z) = z^2+pe^{-z\tau }+q$ and $f_2(z) = z^2+pz e^{-z\tau }+q$, where $p$ and $q$ are real numbers and $\tau >0$. The obtained theorems describe the explicit stability dependence on the changing delay $\tau $. Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained.
AMSclassification: primary 34K20; secondary 34K25.
Keywords: characteristic equation, delay, stability switch.
DOI: 10.5817/AM2023-1-77