TY - JOUR
T1 - Quasi-equilibrium reduction in a general class of stoichiometric producer-consumer models
AU - Stech, Harlan
AU - Peckham, Bruce
AU - Pastor, John
PY - 2012/3
Y1 - 2012/3
N2 - 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.
AB - 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.
KW - energy and nutrient enrichment
KW - producer-consumer models
KW - stoichiometry
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U2 - 10.1080/17513758.2012.713124
DO - 10.1080/17513758.2012.713124
M3 - Article
C2 - 22891701
AN - SCOPUS:84868317478
SN - 1751-3758
VL - 6
SP - 992
EP - 1018
JO - Journal of Biological Dynamics
JF - Journal of Biological Dynamics
IS - 2
ER -