Qualitative permanence of Lotka-Volterra equations.
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.
Hofbauer
Josef
J
Department of Mathematics, University Vienna, Nordbergstrasse 15, 1090 Vienna, Austria.
Kon
Ryusuke
R
Saito
Yasuhisa
Y
D004463:Ecology / Q000706:statistics & numerical data; D017753:Ecosystem; D008433:Mathematics; D008954:Models, Biological