Global attractor in competitive Lotka-Volterra systems

Abstract

For autonomous Lotka-Volterra systems of differential equations modelling the dynamics of n competing species, new criteria are established for the existence of a single point global attractor. Under the conditions of these criteria, some of the species will survive and stabilise at a steady state whereas the others, if any, will die out. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.