The Complex Dynamics in a Food Chain Involving Different Functional Responses

Safaa Jawad  Ali; Adwea Naji  Atewi; Raid Kamel  Naji

doi:10.24996/ijs.2022.63.4.32

Authors

Safaa Jawad Ali Institute of Medical Technology/Al-Mansour, Middle Technical University, Baghdad, Iraq https://orcid.org/0000-0002-7522-7117
Adwea Naji Atewi Institute of Medical Technology/Al-Mansour, Middle Technical University, Baghdad, Iraq
Raid Kamel Naji Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.4.32

Keywords:

Chaos, Stability, Holling type IV, Leslie-Gower, Persistence

Abstract

A food chain model in which the top predator growing logistically has been proposed and studied. Two types of Holling’s functional responses type IV and type II have been used in the first trophic level and second trophic level respectively, in addition to Leslie-Gower in the third level. The properties of the solution are discussed. Since the boundary dynamics are affecting the dynamical behavior of the whole dynamical system, the linearization technique is used to study the stability of the subsystem of the proposed model. The persistence conditions of the obtained subsystem of the food chain are established. Finally, the model is simulated numerically to understand the global dynamics of the food chain under study.