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On an Invasive Species Model with Harvesting

In: Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment

Author

Listed:
  • Sándor Kovács

    (Eötvös Loránd University, Department of Numerical Analysis)

  • Szilvia György

    (Eötvös Loránd University)

  • Noémi Gyúró

    (Eötvös Loránd University)

Abstract

In this paper, a mathematical model will be studied that describes the connections between three species: people, trees, and rats. This model, consisting of a three-dimensional system of ordinary differential equations, has been motivated by attempts to explain the ecological disaster of Easter Island. The system has four equilibria from which three ones are on the boundary of the positive octant of the phase space and—under appropriate conditions—there is a unique interior equilibrium. The existence, uniqueness, and boundedness of the solutions are established. We study the local asymptotical stability of the equilibria and show that Hopf bifurcation takes place: limit cycles occur.

Suggested Citation

  • Sándor Kovács & Szilvia György & Noémi Gyúró, 2020. "On an Invasive Species Model with Harvesting," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment, pages 299-334, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-46306-9_19
    DOI: 10.1007/978-3-030-46306-9_19
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