Document Detail


Daphnia revisited: local stability and bifurcation theory for physiologically structured population models explained by way of an example.
MedLine Citation:
PMID:  19771433     Owner:  NLM     Status:  In-Process    
Abstract/OtherAbstract:
We consider the interaction between a general size-structured consumer population and an unstructured resource. We show that stability properties and bifurcation phenomena can be understood in terms of solutions of a system of two delay equations (a renewal equation for the consumer population birth rate coupled to a delay differential equation for the resource concentration). As many results for such systems are available (Diekmann et al. in SIAM J Math Anal 39:1023-1069, 2007), we can draw rigorous conclusions concerning dynamical behaviour from an analysis of a characteristic equation. We derive the characteristic equation for a fairly general class of population models, including those based on the Kooijman-Metz Daphnia model (Kooijman and Metz in Ecotox Env Saf 8:254-274, 1984; de Roos et al. in J Math Biol 28:609-643, 1990) and a model introduced by Gurney-Nisbet (Theor Popul Biol 28:150-180, 1985) and Jones et al. (J Math Anal Appl 135:354-368, 1988), and next obtain various ecological insights by analytical or numerical studies of special cases.
Authors:
Odo Diekmann; Mats Gyllenberg; J A J Metz; Shinji Nakaoka; Andre M de Roos
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Publication Detail:
Type:  Journal Article; Research Support, Non-U.S. Gov't     Date:  2009-09-22
Journal Detail:
Title:  Journal of mathematical biology     Volume:  61     ISSN:  1432-1416     ISO Abbreviation:  J Math Biol     Publication Date:  2010 Aug 
Date Detail:
Created Date:  2010-05-31     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7502105     Medline TA:  J Math Biol     Country:  Germany    
Other Details:
Languages:  eng     Pagination:  277-318     Citation Subset:  IM    
Affiliation:
Department of Mathematics, University of Utrecht, P. O. Box 80010, 3508 TA, Utrecht, The Netherlands. O.Diekmann@uu.nl
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