Claude Lobry, Frederic Mazenc
Abstract:
An ecological model describing the competition for a single substrate
of an arbitrary number of species is considered.
The mortality rates of the species are not supposed to have all the
same value and the growth function of the substrate is not supposed
to be linear or decreasing.
Intra-specific competition is taken into account. Under additional
technical assumptions, we establish that the model admits a globally
asymptotically stable positive equilibrium point. This ensures
persistence of the species. Our proof relies on a Lyapunov function.
Submitted May 14, 2007. Published September 24, 2007.
Math Subject Classifications: 92B05, 92D25.
Key Words: Species coexistence; ecology; population dynamics.
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Claude Lobry Projet MERE INRIA-INRA UMR Analyse des Systèmes et Biométrie INRA 2, pl. Viala, 34060 Montpellier, France email: claude.lobry@inria.fr |
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Frédéric Mazenc Projet MERE INRIA-INRA UMR Analyse des Systèmes et Biométrie INRA 2, pl. Viala, 34060 Montpellier, France email: mazenc@ensam.inra.fr |
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