Oscillation and global attractivity in hematopoiesis model with periodic coefficients.
type: Item
instance of: scholarly article
title: Oscillation and global attractivity in hematopoiesis model with periodic coefficients.
zbMATH Open document ID: 1048.34114
DOI: 10.1016/S0096-3003(02)00315-6
published in: Applied Mathematics and Computation
publication date: 2003-07-30T00:00:00Z
review text: The author considers the following nonlinear delay differential equation \[ p'(t)= {\beta(t) p^m(t- k\omega)\over 1+ p^n(t- k\omega)}- \gamma(t) p(t),\tag{1} \] where \(k\) is a positive integer, \(\beta(t)\) and \(\gamma(t)\) are positive periodic functions of period \(\omega\). The main result for the nondelay case is Theorem 2.1, where the author proves that (1) has a unique positive periodic solution \(\overline p(t)\). He also studies the global attractivity of \(\overline p(t)\). In the delay case, sufficient conditions for the oscillation of all positive solutions to (1) about \(\overline p(t)\) are given, also some sufficient conditions for the global attractivity of \(\overline p(t)\) are established. It should be noted that (1) is a modification of an equation proposed as a model of hematopoiesis. Similar equations are also used as models in population dynamics.
reviewed by: V. Petrov
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 34K60
zbMATH DE Number: 1957166
zbMATH Keywords: oscillation
zbMATH Keywords: global attractivity
zbMATH Keywords: hematopoiesis
author: S. H. Saker
MaRDI profile type: Publication
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full work available at URL: s0096-3003(02)00315-6
OpenAlex ID: W2130213821
description: scientific article; zbMATH DE number 1957166