A Rosenzweig-MacArthur (1963) Criterion for the Chemostat

The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al....

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Autores principales: Lindström, Torsten, Cheng, Yuanji
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2016
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4967874/
https://www.ncbi.nlm.nih.gov/pubmed/27517080
http://dx.doi.org/10.1155/2016/5626980
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author Lindström, Torsten
Cheng, Yuanji
author_facet Lindström, Torsten
Cheng, Yuanji
author_sort Lindström, Torsten
collection PubMed
description The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al. (1998)), like the chemostat model. In this paper we use the implicit function theorem and implicit derivatives for proving that a similar graphical criterion holds under chemostat conditions, too.
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spelling pubmed-49678742016-08-11 A Rosenzweig-MacArthur (1963) Criterion for the Chemostat Lindström, Torsten Cheng, Yuanji ScientificWorldJournal Research Article The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al. (1998)), like the chemostat model. In this paper we use the implicit function theorem and implicit derivatives for proving that a similar graphical criterion holds under chemostat conditions, too. Hindawi Publishing Corporation 2016 2016-07-18 /pmc/articles/PMC4967874/ /pubmed/27517080 http://dx.doi.org/10.1155/2016/5626980 Text en Copyright © 2016 T. Lindström and Y. Cheng. https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Lindström, Torsten
Cheng, Yuanji
A Rosenzweig-MacArthur (1963) Criterion for the Chemostat
title A Rosenzweig-MacArthur (1963) Criterion for the Chemostat
title_full A Rosenzweig-MacArthur (1963) Criterion for the Chemostat
title_fullStr A Rosenzweig-MacArthur (1963) Criterion for the Chemostat
title_full_unstemmed A Rosenzweig-MacArthur (1963) Criterion for the Chemostat
title_short A Rosenzweig-MacArthur (1963) Criterion for the Chemostat
title_sort rosenzweig-macarthur (1963) criterion for the chemostat
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4967874/
https://www.ncbi.nlm.nih.gov/pubmed/27517080
http://dx.doi.org/10.1155/2016/5626980
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