Coexistence of Competing Species for Intermediate Dispersal Rates in a Reaction–Diffusion Chemostat Model

  • Junping Shi
  • Yixiang Wu
  • Xingfu ZouEmail author


A diffusive chemostat model with two competing species and one nutrient is revisited in this paper. It is shown that at large diffusion rate, both species are washed out, while competition exclusion occurs at small diffusion rate. This implies that a stable coexistence only occurs at intermediate diffusion rate, and an explicit way of determining parameter ranges which support a stable coexistence steady state is given.


Chemostat Reaction–diffusion Competitive exclusion Coexistence Diffusion rate Stability 

Mathematics Subject Classification

35K57 35Q92 35B40 35B35 92D40 



The authors would like to thank the anonymous referee for his valuable comments which have led to a significant improvement in the presentation of the paper.


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Authors and Affiliations

  1. 1.Department of MathematicsCollege of William and MaryWilliamsburgUSA
  2. 2.Department of Applied MathematicsUniversity of Western OntarioLondonCanada
  3. 3.Department of MathematicsVanderbilt UniversityNashvilleUSA

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