Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling

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We consider plankton-nutrient interaction models consisting of phytoplankton, herbivorous zooplankton and dissolved limiting nutrient with general nutrient uptake functions and instantaneous nutrient recycling. For the model with constant nutrient input and different constant washout rates, conditions for boundedness of the solutions, existence and stability of non-negative equilibria, as well as persistence are given. We also consider the zooplankton-phytoplankton-nutrient interaction models with a fluctuating nutrient input and with a periodic washout rate, respectively. It is shown that coexistence of the zooplankton and phytoplankton may arise due to positive bifurcating periodic solutions.

Original languageEnglish (US)
Pages (from-to)633-654
Number of pages22
JournalJournal of Mathematical Biology
Issue number6
StatePublished - Jul 1993
Externally publishedYes



  • Bifurcation
  • Coexistence
  • Fluctuating nutrient input
  • Nutrient recycling
  • Persistence

ASJC Scopus subject areas

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

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