Document Detail

Quasi-equilibrium reduction in a general class of stoichiometric producer-consumer models.
MedLine Citation:
PMID:  22891701     Owner:  NLM     Status:  In-Data-Review    
This article compares a general closed nutrient, stoichiometric producer-consumer model to a two-dimensional 'quasi-equilibrium' approximation. We demonstrate that the quasi-equilibrium system can be rigorously analysed, resulting in nullcline-based criteria for the local stability of system equilibria and for the non-existence of periodic orbits. These results are applied to a study of the dependence of the reduced system on nutrient and energy enrichment. When energy and nutrient enrichment are considered together, the associated bifurcation structures of the two models are seen to share the same essential qualitative characteristics. However, numerical simulations of the three-dimensional parent model show highly complex domains of the persistence and extinction that by Poincare-Bendixson theory are not possible for the two-dimensional reduction. This complexity demonstrates a major difference between the two models, and suggests potential challenges in the use of either model for predicting the long-term behaviour of real-world systems at specific nutrient and energy levels.
Harlan Stech; Bruce Peckham; John Pastor
Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Journal of biological dynamics     Volume:  6     ISSN:  1751-3766     ISO Abbreviation:  J Biol Dyn     Publication Date:  2012 Mar 
Date Detail:
Created Date:  2012-08-15     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101299725     Medline TA:  J Biol Dyn     Country:  England    
Other Details:
Languages:  eng     Pagination:  992-1018     Citation Subset:  IM    
a Department of Mathematics and Statistics , University of Minnesota Duluth , Duluth , MN , 55812 , USA.
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