On the Stability of Four Dimensional Lotka-Volterra Prey-Predator System

A. G. Farhan; Alla Tariq Balasim; Sadiq Al-Nassir

doi:10.24996/ijs.2023.64.8.33

Authors

A. G. Farhan Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq
Alla Tariq Balasim Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0002-6533-1703
Sadiq Al-Nassir Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.8.33

Keywords:

Basin of attraction, Equilibrium points, Lyapunov function, Local stability, Prey-Predator

Abstract

The aim of this work is to study a modified version of the four-dimensional Lotka-Volterra model. In this model, all of the four species grow logistically. This model has at most sixteen possible equilibrium points. Five of them always exist without any restriction on the parameters of the model, while the existence of the other points is subject to the fulfillment of some necessary and sufficient conditions. Eight of the points of equilibrium are unstable and the rest are locally asymptotically stable under certain conditions, In addition, a basin of attraction found for each point that can be asymptotically locally stable. Conditions are provided to ensure that all solutions are bounded. Finally, numerical simulations are given to verify and support the obtained theoretical results.