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Volume 5,     Number 2,     Spring 1997

 

PERMANENCE OF THREE COMPETITORS IN
SEASONAL ECOLOGICAL MODELS WITH
SPATIAL HETEROGENEITY
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.

 

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