Global stability in chemostat-type competition models with nutrient recycling

Shigui Ruan*, Xue Zhong He

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)


Freedman and Xu [J. Math. Biol., 31 (1993), pp. 513-527] proposed two chemostat-type competition models with nutrient recycling. In the first model the recycling is instantaneous whereas in the second, the recycling is delayed. They carried out the equilibrium anaysis and obtained persistence criteria for the models. In this paper, by applying the method of Liapunov functionals we study the global asymptotic stability of the positive equilibria of the models. We also generalize the results to the multispecies competition models with instantaneous and delayed nutrient recycling, respectively. Differing from the dynamics of the usual chemostat models we find that the competing populations could coexist if there is nutrient recycling and they compete directly.

Original languageEnglish
Pages (from-to)170-192
Number of pages23
JournalSIAM Journal on Applied Mathematics
Issue number1
Publication statusPublished - Feb 1998
Externally publishedYes


  • Competition model
  • Global stability
  • Liapunov functional
  • Nutrient recycling
  • Time delay


Dive into the research topics of 'Global stability in chemostat-type competition models with nutrient recycling'. Together they form a unique fingerprint.

Cite this