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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.

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Dynamical Properties of a Seasonally Forced Phytoplankton-Zooplankton Model

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  • 发表日期：

    2025年

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  • Sándor Kovács,
  • Szilvia György

摘要

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.