On Stability of Delay Equations with Positive and Negative Coefficients with Applications

Leonid Berezansky; Elena Braverman

doi:10.4171/zaa/1633

JournalszaaVol. 38, No. 2pp. 157–189

On Stability of Delay Equations with Positive and Negative Coefficients with Applications

Leonid Berezansky
Ben-Gurion University of the Negev, Beer-Sheva, Israel
Elena Braverman
University of Calgary, Canada

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Abstract

We obtain new explicit exponential stability conditions for linear scalar equations with positive and negative delayed terms

\overset{x}{˙} (t) + k = 1 \sum m a_{k} (t) x (h_{k} (t)) - k = 1 \sum l b_{k} (t) x (g_{k} (t)) = 0

and its modifications, and apply them to investigate local stability of Mackey–Glass type models

\overset{x}{˙} (t) = r (t) [β \frac{x ( g ( t ))}{1 + x ^{n} ( g ( t ))} - γ x (h (t))]

and

\overset{x}{˙} (t) = r (t) [β \frac{x ( g ( t ))}{1 + x ^{n} ( h ( t ))} - γ x (t)],

Cite this article

Leonid Berezansky, Elena Braverman, On Stability of Delay Equations with Positive and Negative Coefficients with Applications. Z. Anal. Anwend. 38 (2019), no. 2, pp. 157–189

DOI 10.4171/ZAA/1633