Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A global stability criterion for a family of delayed population models

Authors: Eduardo Liz, Manuel Pinto, Victor Tkachenko and Sergei Trofimchuk
Journal: Quart. Appl. Math. 63 (2005), 56-70
MSC (2000): Primary 34K20; Secondary 92D25
DOI: https://doi.org/10.1090/S0033-569X-05-00951-3
Published electronically: January 19, 2005
MathSciNet review: 2126569
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Abstract: For a family of single-species delayed population models, a new global stability condition is found. This condition is sharp and can be applied in both monotone and nonmonotone cases. Moreover, the consideration of variable or distributed delays is allowed. We illustrate our approach on the Mackey-Glass equations and the Lasota-Wazewska model.

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Eduardo Liz
Affiliation: Departamento de Matemática Aplicada II, E.T.S.I. Telecomunicación, Universidad de Vigo, Campus Marcosende, 36280 Vigo, Spain
Email: eliz@dma.uvigo.es

Manuel Pinto
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile
Email: pintoj@abello.dic.uchile.cl

Victor Tkachenko
Affiliation: Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs’ka str. 3, Kiev, Ukraine
Email: vitk@imath.kiev.ua

Sergei Trofimchuk
Affiliation: Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
Email: trofimch@inst-mat.utalca.cl

DOI: https://doi.org/10.1090/S0033-569X-05-00951-3
Keywords: Global stability, delay differential equations, Schwarz derivative, Mackey-Glass equations, Lasota--Wazewska model
Received by editor(s): January 15, 2004
Published electronically: January 19, 2005
Article copyright: © Copyright 2005 Brown University

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