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

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Abstract

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.

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Acknowledgements

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.

Author information

Correspondence to Xingfu Zou.

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Research supported by NSF of USA (Grant No. DMS-1313243), by a Fields Institute Postdoctoral Fellowship and by NSERC of Canada (Grant No. RGPIN-2016-04665).

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Shi, J., Wu, Y. & Zou, X. Coexistence of Competing Species for Intermediate Dispersal Rates in a Reaction–Diffusion Chemostat Model. J Dyn Diff Equat (2019). https://doi.org/10.1007/s10884-019-09763-0

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Keywords

  • Chemostat
  • Reaction–diffusion
  • Competitive exclusion
  • Coexistence
  • Diffusion rate
  • Stability

Mathematics Subject Classification

  • 35K57
  • 35Q92
  • 35B40
  • 35B35
  • 92D40