Hopf bifurcation for delayed prey-predator system with Allee effect
Abstract
In this study, we take into account a predator-prey system with two delays, the prey is sea urchins and the predator is crabs. The focus is given to the Allee effect where the prey population undergoes, the poisoning of few predators, and a fishing effect on both species considered as selective for the prey. We aim to analyze the system’s stability around interior equilibrium using the theory of bifurcations and determine stability intervals related to delays. The theory of normal form and the center manifold are used to determine the direction of the bifurcations. Finally, numerical simulations are given by numerical methods in DDE-Biftool Matlab package to illustrate the theoretical results.
- Published
- 10 April 2023
- Volume
- 2023 (2023)
- License
- CC BY 3.0
Copyright © 2023 Mohamed Hafdane, Juancho A. Collera, Imane Agmour, Youssef El Foutayeni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
M. Hafdane, J. A. Collera, I. Agmour, Y. E. Foutayeni, Hopf bifurcation for delayed prey-predator system with Allee effect, Commun. Math. Biol. Neurosci. 2023 (2023), 36. https://doi.org/10.28919/cmbn/7921
BibTeX
@article{Hafdane2023,
author = {Hafdane, Mohamed and Collera, Juancho A. and Agmour, Imane and Foutayeni, Youssef El},
title = {Hopf bifurcation for delayed prey-predator system with Allee effect},
journal = {Commun. Math. Biol. Neurosci.},
volume = {2023},
year = {2023},
pages = {36},
doi = {10.28919/cmbn/7921}
}