The dynamics of nutrient, toxic phytoplankton, nontoxic phytoplankton and zooplankton model

  • Authors

    • Hasnaa Fiesal Mohammed Hussien Baghdad University
    • Raid Kamel Naji
    • Azhar Abbas Majeed
    2016-02-12
    https://doi.org/10.14419/ijamr.v5i1.5427
  • Aquatic Food Web, HOPF Bifurcation, Local Bifurcation, Stability Analysis.

  • Abstract

    The objective of this paper is to study the dynamical behavior of an aquatic food web system. A mathematical model that includes nutrients, phytoplankton and zooplankton is proposed and analyzed. It is assumed that, the phytoplankton divided into two compartments namely toxic phytoplankton which produces a toxic substance as a defensive strategy against predation by zooplankton, and a nontoxic phytoplankton. All the feeding processes in this food web are formulating according to the Lotka-Volterra functional response. This model is represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global stability conditions of all possible equilibrium points are established. The occurrence of local bifurcation and Hopf bifurcation are investigated. Finally, numerical simulation is used to study the global dynamics of this model.

  • References

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  • How to Cite

    Hussien, H. F. M., Naji, R. K., & Majeed, A. A. (2016). The dynamics of nutrient, toxic phytoplankton, nontoxic phytoplankton and zooplankton model. International Journal of Applied Mathematical Research, 5(1), 48-62. https://doi.org/10.14419/ijamr.v5i1.5427

    Received date: 2015-10-11

    Accepted date: 2016-01-18

    Published date: 2016-02-12