Journal of Mathematical Biology

, Volume 31, Issue 6, pp 633–654

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

  • Shigui Ruan

DOI: 10.1007/BF00161202

Cite this article as:
Ruan, S. J. Math. Biol. (1993) 31: 633. doi:10.1007/BF00161202


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.

Key words

Persistence Coexistence Nutrient recycling Bifurcation Fluctuating nutrient input 

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Shigui Ruan
    • 1
  1. 1.Department of MathematicsUniversity of AlbertaEdmontonCanada
  2. 2.The Fields Institute for Research in Mathematical SciencesWaterlooCanada

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