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Dynamical Properties of a Seasonally Forced Phytoplankton-Zooplankton Model

In: Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells

Author

Listed:
  • Sándor Kovács

    (Eötvös Loránd University, Department of Numerical Analysis)

  • Szilvia György

    (Eötvös Loránd University, Department of Numerical Analysis)

Abstract

This work deals with the qualitative properties of an autonomous system of differential equations, modeling phytoplankton-zooplankton interactions introduced originally by Truscott and Brindley (Bull Math Biol 56:981–998, 1994) and extended by Freund et al. (Ecol Complex 3:129–29, 2006). While in the first case the occurrence of Hopf bifurcation was conjectured, in the second case it was found that the interior equilibrium was locally stable. Our aim is to give a detailed qualitative description of the model which shows that it is well formed, i.e. the positive quadrant of the phase space is invariant, the solutions are bounded, furthermore it will be shown that under specific circumstances the occurrence of periodic solutions is possible.

Suggested Citation

  • Sándor Kovács & Szilvia György, 2025. "Dynamical Properties of a Seasonally Forced Phytoplankton-Zooplankton Model," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells, pages 159-177, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-97461-8_9
    DOI: 10.1007/978-3-031-97461-8_9
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