Geometric stability switch criteria in delay differential equations with two delays and delay dependent parameters
type: Item
instance of: scholarly article
title: Geometric stability switch criteria in delay differential equations with two delays and delay dependent parameters
zbMATH Open document ID: 1414.34056
author: Qi An
author: E. Beretta
author: Yang Kuang
author: Chuncheng Wang
author: Hao Wang
published in: Journal of Differential Equations
publication date: 2019-03-22T00:00:00Z
review text: In considering stability of delay differential equations with two delays at an equilibrium point, the characteristic equation of the linearised delay differential equation may have the form \[P_0(\lambda, \tau) + P_1(\lambda, \tau)e^{-\lambda\tau} +P_2(\lambda, \tau)e^{-\lambda\tau_1} =0,\] where $\tau\in I \subset\mathbb{R}_+, \tau_1\in\mathbb{R}_+, P_{\ell}(\lambda, \tau), \ell = 0, 1, 2$, are polynomials in $\lambda$. In this paper, crossing curves on the $(\tau, \tau_1)$-plane on which the characteristic equation has pure imaginary roots are investigated under certain assumptions. Based on these crossing curves, stability switch can be obtained for the delay parameters $\tau$ and $\tau_1$. Although results on stability switch for equations with one delay $\tau$ can be found in literature, the authors claim that the investigation on stability switch for equations with two delays is new. As an example, stability switch analysis is provided for an epidemic model with two delays.
reviewed by: Zhanyuan Hou
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 7040850
zbMATH Keywords: delay differential equations
zbMATH Keywords: stability switch
zbMATH Keywords: characteristic equation
zbMATH Keywords: epidemic model
MaRDI profile type: Publication
full work available at URL: j.jde.2018.11.025
OpenAlex ID: W2900959448
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DOI: 10.1016/J.JDE.2018.11.025
Wikidata QID: Q128889502
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description: scientific article; zbMATH DE number 7040850