Nutrient-phytoplankton-zooplankton interaction with variable yields

Volume 40 / 2013

Joydeb Bhattacharyya, Samares Pal Applicationes Mathematicae 40 (2013), 327-349 MSC: Primary 92B05; Secondary 92D25. DOI: 10.4064/am40-3-5

Abstract

A three dimensional predator-prey-resource model is proposed and analyzed to study the dynamics of the system with resource-dependent yields of the organisms. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive even in the absence of predation. Local stability of the system is obtained in the absence of one or more of the predators and in the presence of all the predators. Under appropriate circumstances global stability of the system is obtained in the absence of the predator at the highest trophic level. Moreover, it is shown that the system undergoes Hopf bifurcation if the break-even concentration crosses a certain critical value. Computer simulations have been carried out to illustrate various analytical results.

Authors

  • Joydeb BhattacharyyaDepartment of Mathematics
    University of Kalyani
    Kalyani 741235, India
    e-mail
  • Samares PalDepartment of Mathematics
    University of Kalyani
    Kalyani 741235, India
    e-mail

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