Periodic solutions and hydra effect for delay differential equations with nonincreasing feedback
type: Item
instance of: scholarly article
title: Periodic solutions and hydra effect for delay differential equations with nonincreasing feedback
zbMATH Open document ID: 1396.34047
author: Tibor Krisztin
author: Mónika Polner
author: Gabriella Vas
published in: Qualitative Theory of Dynamical Systems
publication date: 2018-02-20T00:00:00Z
full work available at URL: TKMPGV Hydra article.pdf
review text: The authors consider a delay differential equation of the form \[ y'(t)=-\mu y(t)+f(y(t-1)) \] with \(\mu>0\) and a nonincreasing function \(f:\mathbb{R}\to(0,\infty)\). This equation models the change in time of the quantity \(y(t)\geq 0\) such that \(y\) decays with a rate proportional to \(y(t)\), and is produced with a rate \(f(y(t-1))\). The aim of this paper is to show analytically that hydra effect appears in the above equation. This phenomenon was observed recently in different mathematical models in population dynamics and is described by the fact that the size of the population can be increased by increasing the mortality rate.
reviewed by: Adriana Buică
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K27
zbMATH DE Number: 6841281
zbMATH Keywords: delay differential equation
zbMATH Keywords: periodic solution
zbMATH Keywords: mean value
zbMATH Keywords: hydra effect
zbMATH Keywords: nonincreasing feedback
MaRDI profile type: Publication
OpenAlex ID: W2300997184
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DOI: 10.1007/S12346-016-0191-2
description: scientific article; zbMATH DE number 6841281