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

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Abstract

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

x˙(t)+k=1mak(t)x(hk(t))k=1lbk(t)x(gk(t))=0\dot{x}(t)+ \sum_{k=1}^m a_k(t)x(h_k(t))- \sum_{k=1}^l b_k(t)x(g_k(t))=0

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

x˙(t)=r(t)[βx(g(t))1+xn(g(t))γx(h(t))]\dot{x}(t)=r(t)\left[\beta\frac{x(g(t))}{1+x^n(g(t))}-\gamma x(h(t))\right]

and

x˙(t)=r(t)[βx(g(t))1+xn(h(t))γx(t)],\dot{x}(t)=r(t)\left[\beta\frac{x(g(t))}{1+x^n(h(t))}-\gamma x(t)\right],

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