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

Sándor Kovács (), Szilvia György and Noémi Gyúró
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Sándor Kovács: Eötvös Loránd University, Department of Numerical Analysis
Szilvia György: Eötvös Loránd University
Noémi Gyúró: Eötvös Loránd University

A chapter in Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells, 2021, pp 17-31 from Springer

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-73241-7_2

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DOI: 10.1007/978-3-030-73241-7_2

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