Qualitative permanence of Lotka-Volterra equations

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

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.

MeSH terms

  • Ecology / statistics & numerical data
  • Ecosystem*
  • Mathematics
  • Models, Biological*