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An extremum principle for parabolic competition

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Abstract

Parabolic growth invariably results in the survival of all competing types. Under the constraint of constant total concentration, there is a unique equilibrium in the simplex interior, which is asymptotically stable inside the whole simplex. The appropriate Lyapunov function is obtained in terms of the excess productivity which is shown to be maximized for the competitive system with fractional order kinetics. Claims to the contrary are refuted.

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Authors and Affiliations

  1. Collegium Budapest (Institute for Advanced Study), 2 Szentháromság utca, H-1014, Budapest, Hungary

    Zoltán Varga & Eörs Szathmáry

  2. Department of Mathematics, University of Agricultural Sciences, H-2103, Gödöllő, Hungary

    Zoltán Varga

  3. Deaprtment of Plant Taxonomy and Ecology, Eötvös University, 2 Ludovika tér, H-1083, Budapest, Hungary

    Eörs Szathmáry

Authors
  1. Zoltán Varga
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  2. Eörs Szathmáry
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Varga, Z., Szathmáry, E. An extremum principle for parabolic competition. Bltn Mathcal Biology 59, 1145–1154 (1997). https://doi.org/10.1007/BF02460105

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  • DOI: https://doi.org/10.1007/BF02460105

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