A necessary and sufficient condition for permanence of a Lotka-Volterra discrete system with delays

Abstract

In this paper we consider the permanence of the following Lotka-Volterra discrete competition system with delays k1, k2, l1, and l2: x(n+1)=x(n)expr1[1-x(n-k1)-μ1y(n-k2)], y(n+1)=y(n)expr2[1-μ2x(n-l1)-y(n-l2)]. We show the system is permanent for all nonnegative integers k1, k2, l1, and l2, if and only if μ1<1 and μ2<1 hold. © 2001 Academic Press.