Dynamics of competitive systems with a single common limiting factor

Ryusuke Kon

doi:10.3934/mbe.2015.12.71

Article Contents

2015, Volume 12, Issue 1: 71-81. Doi: 10.3934/mbe.2015.12.71

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Dynamics of competitive systems with a single common limiting factor

Ryusuke Kon^1,

1.
Faculty of Engineering, University of Miyazaki, Gakuen Kibanadai Nishi 1-1, Miyazaki 889-2192

Received: March 31, 2014

Revised: September 30, 2014

Published: November 2014

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Abstract

The concept of limiting factors (or regulating factors) succeeded in formulating the well-known principle of competitive exclusion. This paper shows that the concept of limiting factors is helpful not only to formulate the competitive exclusion principle, but also to obtain other ecological insights. To this end, by focusing on a specific community structure, we study the dynamics of Kolmogorov equations and show that it is possible to derive an ecologically insightful result only from the information about interactions between species and limiting factors. Furthermore, we find that the derived result is a generalization of the preceding work by Shigesada, Kawasaki, and Teramoto (1984), who examined a certain Lotka-Volterra equation in a different context.

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Mathematics Subject Classification: Primary: 34D20; Secondary: 92B05.

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