Coexistence for a resource-based growth model with two resources

Abstract

We investigate the coexistence of positive steady-state solutions to a parabolic system, which models a single species on two growth-limiting, non-reproducing resources in an un-stirred chemostat with diffusion. We establish the existence of a positive steady-state solution for a range of the parameter $(m,n)$, the bifurcation solutions and the stability of bifurcation solutions. The proof depends on the maximum principle, bifurcation theorem and perturbation theorem.