Periodic response to periodic forcing of the Droop equations for phytoplankton growth

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The dynamics of a phytoplankton population growing in a chemostat under a periodic supply of nutrients is investigated with the model proposed by Droop. This model differs from the well-known Monod equations by incorporating nutrient storage by the cells. In spite of its nonlinearity and the time delays introduced by an internal nutrient pool, the model predicts a simple response to a periodic nutrient supply. The population is shown to oscillate with the same frequency as the forcing. To prove the existence of a periodic solution local and global bifurcation results are used. This work establishes a basis on which to evaluate experimental data against the model as a representation of the nutrient-phytoplankton interaction when nutrients fluctuate.

Original languageEnglish (US)
Pages (from-to)743-759
Number of pages17
JournalJournal Of Mathematical Biology
Issue number8
StatePublished - Oct 1994


  • Global bifurcation result
  • Nutrient variability
  • Periodic solution
  • Phytoplankton
  • Population dynamics

ASJC Scopus subject areas

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


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