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Permanence of some ecological systems with several predator and one prey species

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Abstract

The stability criterion used in the following is “permanence”. Permanence means that all trajectories starting in the interior are ultimately bounded away from the boundary and that this bound is independent of the initial values. Hence sufficiently small fluctuations cannot lead to extinction of any species. In the following we deal with one-prey, two-predator resp. one-prey, three-predator systems and a one-prey, two-predator, one-top-predator system with three trophic levels. It turns out that the characterization of permanence for such models described by Lotka-Volterra dynamics is rather simple and elegant.

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  1. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria

    Gabriela Kirlinger

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  1. Gabriela Kirlinger
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Kirlinger, G. Permanence of some ecological systems with several predator and one prey species. J. Math. Biology 26, 217–232 (1988). https://doi.org/10.1007/BF00277734

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