# On The Mathematical Model of Two- Prey and Two-Predator Species

• A. G. Frahan Department of Math., College of Basic Education, Mustansiriyah University, Baghdad, Iraq
Keywords: Prey-Predator, Switching, Group defense, Equilibrium point, Local stability, Basin of attraction

### Abstract

In this work, we study two species of predator with two species of prey model, where the two species of prey live in two diverse habitats and have the ability to group-defense. Only one of the two predators tends to switch between the habitats. The mathematical model has at most 13 possible equilibrium points, one of which is the point of origin, two are axial, tow are interior points and the others are boundary points. The model with , where n is the switching index, is discussed regarding the boundedness of its solutions and the local stability of its equilibrium points. In addition, a basin of attraction was created for the interior point. Finally, three numerical examples were given to support the theoretical results.

Published
2020-03-27
How to Cite
Frahan, A. G. (2020). On The Mathematical Model of Two- Prey and Two-Predator Species. Iraqi Journal of Science, 61(3), 608-619. https://doi.org/10.24996/ijs.2020.61.3.17
Issue
Section
Mathematics  