Reaction–diffusion equations of two species competing for two complementary resources with internal storage

This paper examines a system of reaction–diffusion equations arising from a mathematical model of two microbial species competing for two complementary resources with internal storage in an unstirred chemostat. The governing system can be reduced to a limiting system based on two uncoupled conservation principles. One of main technical difficulties in our analysis is the singularities in the reaction terms. Conditions for persistence of one population and coexistence of two competing populations are derived from eigenvalue problems, maximum principle and the theory of monotone dynamical systems.