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Oscillatory Behavior of a Delayed Ratio-Dependent Predator–Prey System with Michaelis–Menten Functional Response

In: Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells

Author

Listed:
  • Sándor Kovács

    (Eötvös Loránd University, Department of Numerical Analysis)

  • Szilvia György

    (Eötvös Loránd University)

  • Noémi Gyúró

    (Eötvös Loránd University)

Abstract

In this chapter, a mathematical model will be studied, which describes predator–prey relations. This model, consisting of a higher dimensional system of ordinary differential equations, has been motivated by ecological systems in which more different predator species are competing for a single-prey species. In order to have a more realistic model, an infinite distributed delay will be introduced into the prey’s density. This delay takes into account that the predator’s growth rate at present depends on past quantities of prey. We investigate under what conditions does the originally asymptotically stable interior equilibrium lose its stability and prove the occurrence of limit cycles.

Suggested Citation

  • Sándor Kovács & Szilvia György & Noémi Gyúró, 2021. "Oscillatory Behavior of a Delayed Ratio-Dependent Predator–Prey System with Michaelis–Menten Functional Response," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells, pages 17-31, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-73241-7_2
    DOI: 10.1007/978-3-030-73241-7_2
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