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Dynamics of competitive systems with a single common limiting factor. (English) Zbl 1321.34064

Summary: 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 N. Shigesada et al. [J. Math. Biol. 21, 97–113 (1984; Zbl 0568.92017)], who examined a certain Lotka-Volterra equation in a different context.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34D20 Stability of solutions to ordinary differential equations
92D25 Population dynamics (general)
92D40 Ecology

Citations:

Zbl 0568.92017
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References:

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