Title: Bifurcation and stability of a dynamical system with threshold prey harvesting

Authors: Imane Agmour; Meriem Bentounsi; Naceur Achtaich; Youssef El Foutayeni

Addresses: Analysis, Modeling and Simulation Laboratory, Hassan II University of Casablanca, Morocco ' Analysis, Modeling and Simulation Laboratory, Hassan II University of Casablanca, Morocco ' Analysis, Modeling and Simulation Laboratory, Hassan II University of Casablanca, Morocco ' Analysis, Modeling and Simulation Laboratory, Hassan II University of Casablanca, Morocco; Unit for Mathematical and Computer Modeling of Complex Systems, IRD, France

Abstract: In this study, a predator-prey interaction model with Holling type II functional response is studied. As the continuous threshold prey harvesting is introduced, the proposed model displays a dynamics in the predator-prey plane. The main purpose is to show how the stability properties of some coexistence equilibria could be directly affected by harvesting. As the results, we find out that the proposed system exhibits saddle node bifurcation, subcritical and supercritical Hopf bifurcations under some conditions. The local bifurcation solutions for different parameters of the model are obtained via bifurcation theory.

Keywords: predator-prey interaction model; Holling type II functional response; stability; bioeconomic equilibria; bifurcations.

DOI: 10.1504/IJCSM.2021.118075

International Journal of Computing Science and Mathematics, 2021 Vol.14 No.1, pp.36 - 53

Received: 17 Sep 2018
Accepted: 02 Jan 2019
Published online: 12 Oct 2021 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article