Journal of Mathematical Biology

, Volume 18, Issue 3, pp 255–280

Competition for fluctuating nutrient

  • J. K. Hale
  • A. S. Somolinos


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.

Key words

Population dyamics Ecology Periodic solutions 


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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • J. K. Hale
    • 1
  • A. S. Somolinos
    • 2
  1. 1.Lefschetz Center for Dynamical Systems, Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Brown University from Universidad de Alcala de HenaresMadridSpain

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