Mathematical Biosciences and Engineering, 2015, 12(1): 71-81. doi: 10.3934/mbe.2015.12.71.

Primary: 34D20; Secondary: 92B05.

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Dynamics of competitive systems with a single common limiting factor

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

   

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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Keywords nonlinear complementary problem; saturated equilibrium; Lotka-Volterra equation.; P-function; P-matrix

Citation: Ryusuke Kon. Dynamics of competitive systems with a single common limiting factor. Mathematical Biosciences and Engineering, 2015, 12(1): 71-81. doi: 10.3934/mbe.2015.12.71

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Copyright Info: 2015, Ryusuke Kon, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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