Uniqueness of limit cycles for a limiting case of the chemostat : does it justify the use of logistic growth rates?

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Uniqueness of limit cycles for a limiting case of the chemostat : does it justify the use of logistic growth rates?

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Publication Article, peer reviewed scientific
Title Uniqueness of limit cycles for a limiting case of the chemostat : does it justify the use of logistic growth rates?
Author(s) Lindström, Torsten ; Cheng, Yuanji
Date 2015
English abstract
On infinitesimally short time intervals various processes contributing to population change tend to operate independently so that we can simply add their contributions (Metz and Diekmann, The dynamics of physiologically structured populations, 1986, p. 3). This is one of the cornerstones for differential equations modeling in general. Complicated models for processes interacting in a complex manner may be built up, and not only in population dynamics. The principle holds as long as the various contributions are taken into account exactly. In this paper we discuss commonly used approximations that may lead to non-removable dependency terms potentially affecting the long run qualitative behavior of the involved equations. We prove that these terms do not produce such effects in the simplest and most interesting biological case, but the general case is left open. Our main result is a rather complete analysis of an important limiting case. Once complete knowledge of the qualitative properties of simple models is obtained, it greatly facilitates further studies of more complex models. A consequence of our analysis is that standard methods can be applied. However, the application of those methods is far from straightforward and require non-trivial estimates in order to make them valid for all values of the parameters. We focus on making these proofs as elementary as possible.
DOI http://dx.doi.org/10.14232/ejqtde.2015.1.47 (link to publisher's fulltext.)
Publisher Bolyai institute
Host/Issue Electronic Journal of Qualitative Theory of Differential Equations;47
ISSN 1417-3875
Pages 1-14
Language eng (iso)
Subject(s) uniqueness of limit cycles
chemostat model
Sciences
Research Subject Categories::MATHEMATICS
Handle http://hdl.handle.net/2043/19752 (link to this page)

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