Abstract
A model of the competition of n species for a single essential periodically fluctuating nutrient is considered. Instead of the familiar Michaelis-Menten kinetics for nutrient uptake, we assume only that the uptake rate functions are positive, increasing and bounded above. Sufficient conditions for extinction are given. The existence of a nutrient threshold under which the Principle of Competitive Exclusion holds, is proven. For two species systems the following very general result is proven: All solutions of a τ-periodic, dissipative, competitive system are either τ-periodic or approach a τ-periodic solution. A complete description of the geometry of the Poincaré operator of the two species system is given.
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On leave at Brown University from Universidad de Alcala de Henares, Madrid, Spain
This research has been supported in part by the National Science Foundation under contract #MCS 8205355, and in part by the U.S. Army Research Office under contract #DAAG-29-79-C-0161
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Hale, J.K., Somolinos, A.S. Competition for fluctuating nutrient. J. Math. Biology 18, 255–280 (1983). https://doi.org/10.1007/BF00276091
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DOI: https://doi.org/10.1007/BF00276091