The periodically forced Droop model for phytoplankton growth in a chemostat

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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
DOIs
StatePublished - May 1997

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Keywords

  • Chemostat
  • Droop model
  • Global stability
  • Phytoplankton

ASJC Scopus subject areas

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

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