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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Extinction in competitive Lotka-Volterra systems


Author: M. L. Zeeman
Journal: Proc. Amer. Math. Soc. 123 (1995), 87-96
MSC: Primary 92D25; Secondary 34C05, 34D20, 34D45, 92D40
MathSciNet review: 1264833
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Abstract: It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to arbitrary finite dimension. That is, for the n-species autonomous competitive Lotka-Volterra model, we exhibit simple algebraic criteria on the parameters which guarantee that all but one of the species is driven to extinction, whilst the one remaining population stabilises at its own carrying capacity.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1264833-2
PII: S 0002-9939(1995)1264833-2
Article copyright: © Copyright 1995 American Mathematical Society