Stability Analysis of a Prey-Predator Model with Prey Refuge and Fear of Adult Predator

Salam Jasim Majeed; Sarah Fawzi Ghafel

doi:10.24996/ijs.2022.63.10.24

Authors

Salam Jasim Majeed Department of Mathematics, College of Computer Science and Mathematics, University of Thi-Qar, Thi-Qar, Iraq
Sarah Fawzi Ghafel Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar ,Thi-Qar, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.10.24

Keywords:

Equilibrium points, Stability analysis, Fear effect

Abstract

This paper is concerned with a Holling-II stage-structured predator-prey system in which predators are divided into an immature and mature predators. The aim is to explore the impact of the prey's fear caused by the dread of mature predators in a prey-predator model including intraspecific competitions and prey shelters. The theoretical study includes the local and global stability analysis for the three equilibrium points of the system and shows the prey's fear may lead to improving the stability at the positive equilibrium point. A numerical analysis is given to ensure the accuracy of the theoretical outcomes and to testify the conditions of stability of the system near the non-trivial equilibrium points.