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The Scientific World Journal
Volume 2016 (2016), Article ID 5626980, 6 pages
http://dx.doi.org/10.1155/2016/5626980
Research Article

A Rosenzweig-MacArthur (1963) Criterion for the Chemostat

1Department of Mathematics, Linnaeus University, 35195 Växjö, Sweden
2School of Technology, Malmö University, 20506 Malmö, Sweden

Received 29 April 2016; Accepted 6 June 2016

Academic Editor: Tuncay Candan

Copyright © 2016 Torsten Lindström and Yuanji Cheng. 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.

Abstract

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.