A generalization of the three-dimensional Bernfeld-Haddock conjecture and its proof
type: Item
instance of: scholarly article
title: A generalization of the three-dimensional Bernfeld-Haddock conjecture and its proof
zbMATH Open document ID: 1209.34092
author: Qiyuan Zhou
author: Wentao Wang
author: Qiyi Fan
published in: Journal of Computational and Applied Mathematics
publication date: 2009-10-09T00:00:00Z
review text: This paper deals with the following system of delay differential equations \[ x'_1(t)=-F(x_1(t))+G(x_2(t-r_2)), \] \[ x'_2(t)=-F(x_2(t))+G(x_3(t-r_3)), \] \[ x'_3(t)=-F(x_3(t))+G(x_1(t-r_1)), \] where \(r_1, r_2\) and \(r_3\) are positive constants, and \(F\) is nondecreasing on \(\mathbb R^1\). Such a system is related to a three-dimensional generalization of the Bernfeld-Haddock conjecture. By means of the monotone technique, the authors find that each bounded solution of the systems tends to a constant vector under some desirable conditions.
reviewed by: Mingshu Peng
Mathematics Subject Classification ID: 34K25
zbMATH DE Number: 5612615
zbMATH Keywords: Bernfeld-Haddock conjecture
zbMATH Keywords: delay differential equation
zbMATH Keywords: asymptotic constancy
Wikidata QID: Q123204660
MaRDI profile type: Publication
full work available at URL: j.cam.2009.07.047
OpenAlex ID: W1971827095
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DOI: 10.1016/J.CAM.2009.07.047
description: scientific article; zbMATH DE number 5612615