The Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species

  • Ekhlas Abd Al-Husain Jabr Department of Mathematics, College of Science, University of Baghdad, Iraq
  • Dahlia Khaled Bahlool Department of Mathematics, College of Science, University of Baghdad, Iraq
Keywords: Food web, prey refuge, Stability, bifurcation, persistence

Abstract

This paper aims to study the role of a prey refuge that depends on both prey and predator species on the dynamics of a food web model. It is assumed that the food transfer among the web levels occurs according to Lotka-Volterra functional response. The solution properties, such as existence, uniqueness, and uniform boundedness, are discussed. The local, as well as the global, stabilities of the solution of the system are investigated. The persistence of the system is studied with the assistance of average Lyapunov function. The local bifurcation conditions that may occur near the equilibrium points are established. Finally, numerical simulation is used to confirm our obtained results. It is observed that the system has only one type of attractors that is a stable point, while periodic dynamics do not exist even on the boundary planes.

Published
2021-02-27
How to Cite
Jabr , E. A. A.-H., & Bahlool, D. K. (2021). The Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species. Iraqi Journal of Science, 62(2), 639-657. https://doi.org/10.24996/ijs.2021.62.2.29
Section
Mathematics