Volume 5, Number 2, Spring 1997
PERMANENCE OF THREE COMPETITORS IN
SEASONAL ECOLOGICAL MODELS WITH
ERIC JOSE AVILA-VALES AND ROBERT STEPHEN CANTRELL
Abstract. We obtain conditions for permanence in a
reaction-diffusion system modelling the interaction of three
competing species in a bounded habitat whose exterior is
lethal to each species under the assumption that the local
inter- and intraspecific interactions are temporally periodic.
Our results are based upon the Hale-Waltman acyclicity theorem,
a skew-product flow approach having been employed to
convert the reaction-diffusion system into a continuous time
semi-dynamical system. The conditions we derive all are expressed
in terms of the sign of the principal eigenvalue for certain
associated periodic-parabolic linear operators and may
be interpreted biologically as invasibility conditions.