PERMANENCE IN KOLMOGOROV-TYPE SYSTEMS OF NONAUTONOMOUS FUNCTIONAL-DIFFERENTIAL EQUATIONS

In this paper we establish some general results on the permanence of t he n-species Kolmogorov-type nonautonomous functional differential sys tem over dot x(i) = x(i)(t)f(i)(t, x(t)), i = 1,2,...,n. These results are applied to the n-species Lotka-Volterra-type systems with distrib uted delays, that is, when f(i)(t, x(t)) are linear functions of x(t). Our method consists of constructing n Liapunov-like functions, which can be regarded as boundary functions of some compact region inside th e positive cone in R(n). (C) 1996 Academic Press, Inc.