In this paper, a set of sufficient conditions are obtained for the existenc
e of a globally asymptotically stable equilibrium point in various submodel
s of the classic n-dimensional Lotka-Volterra system. The submodels are the
following systems: competition (cooperative or predator-prey) chain system
and competition (cooperative or predator-prey) model between one and multi
species. The criteria in this paper are in explicit forms of the parameters
and thus are easily verifiable. (C) 1999 Academic Press.