Global stability in chemostat-type competition models with nutrient recycling

Shigui Ruan, Xue Zhong He

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

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 (US)
Pages (from-to)170-192
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume58
Issue number1
StatePublished - Feb 1998
Externally publishedYes

Fingerprint

Chemostats
Chemostat
Competition Model
Recycling
Global Stability
Nutrients
Instantaneous
Chemostat Model
Global Asymptotic Stability
Lyapunov Functional
Persistence
Asymptotic stability
Model
Generalise

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Global stability in chemostat-type competition models with nutrient recycling. / Ruan, Shigui; He, Xue Zhong.

In: SIAM Journal on Applied Mathematics, Vol. 58, No. 1, 02.1998, p. 170-192.

Research output: Contribution to journalArticle

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