Global stability in chemostat-type plankton models with delayed nutrient recycling

Xue Zhong He, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


In this paper, we consider chemostat-type plankton models in which plankton feeds on a limiting nutrient and the nutrient is supplied at a constant rate and is partially recycled after the death of plankton by bacterial decomposition. We use a distributed delay to describe nutrient recycling and a discrete delay to model the planktonic growth response to nutrient uptake. When one or both delays occur, by constructing Liapunov functionals, we obtain some sufficient conditions for the global attractivity of the positive equilibrium, which can be regarded as estimates of the delays for persistence of global attractivity.

Original languageEnglish (US)
Pages (from-to)253-271
Number of pages19
JournalJournal of Mathematical Biology
Issue number3
StatePublished - Sep 1998
Externally publishedYes


  • Global attractivity
  • Liapunov functionals
  • Nutrient recycling
  • Plankton models
  • Time delay

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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