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

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Abstract

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
Volume31
Issue number6
DOIs
StatePublished - 1993
Externally publishedYes

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Zooplankton
Phytoplankton
Recycling
Nutrients
Coexistence
Persistence
recycling
Instantaneous
zooplankton
phytoplankton
nutrient-nutrient interactions
Food
nutrients
Model
nutrient uptake
Plankton
plankton
Positive Periodic Solution
Stability of Solutions
Rate Constant

Keywords

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

ASJC Scopus subject areas

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

Cite this

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AB - 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.

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