Permanence in kolmogorov-type systems of nonautonomous functional differential equations

Abstract

In this paper we establish some general results on the permanence of the n-species Kolmogorov-type nonautonomous functional differential system ẋi = xi(t)fi(t, xt), i = 1,2,...,n. These results are applied to the n-species Lotka-Volterra-type systems with distributed delays, that is, when fi(t, xt) are linear functions of xt. Our method consists of constructing n Liapunov-like functions, which can be regarded as boundary functions of some compact region inside the positive cone in Rn. © 1996 Academic Press, Inc.