The periodically forced Droop model for phytoplankton growth in a chemostat

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

It is proved that the periodically forced Droop model for phytoplankton growth in a chemostat has precisely two dynamic regimes depending on a threshold condition involving the dilution rate. If the dilution rate is such that the sub-threshold condition holds, the phytoplankton population is washed out of the chemostat. If the super-threshold condition holds, then there is a unique periodic solution, having the same period as the forcing, characterized by the presence of the phytoplankton population, to which all solutions approach asymptotically. Furthermore, this result holds for a general class of models with monotone growth rate and monotone uptake rate, the latter possibly depending on the cell quota.

Original languageEnglish (US)
Pages (from-to)545-556
Number of pages12
JournalJournal of Mathematical Biology
Volume35
Issue number5
StatePublished - May 1997

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Chemostats
Chemostat
Phytoplankton
phytoplankton
Dilution
Monotone
Growth
Population
Forcing
Periodic Solution
Model
Cell
cells

Keywords

  • Chemostat
  • Droop model
  • Global stability
  • Phytoplankton

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

The periodically forced Droop model for phytoplankton growth in a chemostat. / Smith, Hal.

In: Journal of Mathematical Biology, Vol. 35, No. 5, 05.1997, p. 545-556.

Research output: Contribution to journalArticle

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