Nicholson's blowflies differential equations with a small delay in the mortality term

Leonid Berezansky; Elena Braverman

doi:10.1016/j.nonrwa.2024.104193

Nicholson's blowflies differential equations with a small delay in the mortality term

Leonid Berezansky, Elena Braverman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For the Nicholson's blowflies equation with delayed mortality N^′(t)=m(t)−δN(h₁(t))+PN(h₂(t))e^{−γN(h₂(t))},P>δ,positivity, persistence, and boundedness of solutions are established. Two global stability tests for the positive equilibrium are obtained based on a linearized global stability method, reducing stability of a non-linear model to a specially constructed linear equation. The first one extends the absolute stability result to the case of delayed mortality and the second test is delay-dependent.

Original language	English
Article number	104193
Journal	Nonlinear Analysis: Real World Applications
Volume	81
DOIs	https://doi.org/10.1016/j.nonrwa.2024.104193
State	Published - 1 Feb 2025

Keywords

Delay differential equations
Delay-dependent stability conditions
Delayed mortality
Global exponential stability
Nicholson's blowflies equation

ASJC Scopus subject areas

Analysis
General Engineering
General Economics, Econometrics and Finance
Computational Mathematics
Applied Mathematics

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10.1016/j.nonrwa.2024.104193

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title = "Nicholson's blowflies differential equations with a small delay in the mortality term",

abstract = "For the Nicholson's blowflies equation with delayed mortality N′(t)=m(t)−δN(h1(t))+PN(h2(t))e−γN(h2(t)),P>δ,positivity, persistence, and boundedness of solutions are established. Two global stability tests for the positive equilibrium are obtained based on a linearized global stability method, reducing stability of a non-linear model to a specially constructed linear equation. The first one extends the absolute stability result to the case of delayed mortality and the second test is delay-dependent.",

keywords = "Delay differential equations, Delay-dependent stability conditions, Delayed mortality, Global exponential stability, Nicholson's blowflies equation",

author = "Leonid Berezansky and Elena Braverman",

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AU - Braverman, Elena

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N2 - For the Nicholson's blowflies equation with delayed mortality N′(t)=m(t)−δN(h1(t))+PN(h2(t))e−γN(h2(t)),P>δ,positivity, persistence, and boundedness of solutions are established. Two global stability tests for the positive equilibrium are obtained based on a linearized global stability method, reducing stability of a non-linear model to a specially constructed linear equation. The first one extends the absolute stability result to the case of delayed mortality and the second test is delay-dependent.

AB - For the Nicholson's blowflies equation with delayed mortality N′(t)=m(t)−δN(h1(t))+PN(h2(t))e−γN(h2(t)),P>δ,positivity, persistence, and boundedness of solutions are established. Two global stability tests for the positive equilibrium are obtained based on a linearized global stability method, reducing stability of a non-linear model to a specially constructed linear equation. The first one extends the absolute stability result to the case of delayed mortality and the second test is delay-dependent.

KW - Delay differential equations

KW - Delay-dependent stability conditions

KW - Delayed mortality

KW - Global exponential stability

KW - Nicholson's blowflies equation

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SN - 1468-1218

VL - 81

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

M1 - 104193

ER -

Nicholson's blowflies differential equations with a small delay in the mortality term

Abstract

Keywords

ASJC Scopus subject areas

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