Competition for fluctuating nutrient

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, the authors assume only that the uptake rate functions are positive, increasing and bounded above. Sufficient conditi...

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Bibliographic Details
Published in:Journal of mathematical biology 1983-12, Vol.18 (3), p.255-280
Main Authors: HALE, J. K, SOMOLINOS, A. S
Format: Article
Language:English
Subjects:
Animal and plant ecology
Animal, plant and microbial ecology
Animals
Autoecology
Biological and medical sciences
Fundamental and applied biological sciences. Psychology
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Summary: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, the authors 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 tau periodic, dissipative, competitive system are either tau -periodic or approach a tau -periodic solution. A complete description of the geometry of the Poincare operator of the two species system is given.
ISSN:0303-6812
1432-1416
DOI:10.1007/BF00276091