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J Math Biol. 2008 Dec;57(6):863-81. doi: 10.1007/s00285-008-0192-0. Epub 2008 Jun 3.

Qualitative permanence of Lotka-Volterra equations.

Author information

1
Department of Mathematics, University Vienna, Nordbergstrasse 15, 1090 Vienna, Austria.

Abstract

In this paper, we consider permanence of Lotka-Volterra equations. We investigate the sign structure of the interaction matrix that guarantees the permanence of a Lotka-Volterra equation whenever it has a positive equilibrium point. An interaction matrix with this property is said to be qualitatively permanent. Our results provide both necessary and sufficient conditions for qualitative permanence.

PMID:
18521608
DOI:
10.1007/s00285-008-0192-0
[Indexed for MEDLINE]

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