Nonlinear Dynamics and Stability of a Stage-Structured Predator–Prey System with Fear Factors

Bushra E. Kashem; Hassan F. Al-Husseiny; Anwar Zeb

doi:10.30526/38.4.4152

Authors

Bushra E. Kashem Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-0327-7916
Hassan F. Al-Husseiny College of Applied Science, University of Technology, Baghdad, Iraq https://orcid.org/0009-0007-7883-5875
Anwar Zeb Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan https://orcid.org/0000-0002-5460-3718

DOI:

https://doi.org/10.30526/38.4.4152

Keywords:

Prey - Predator System, Stage Structure, Holling type, Harvesting, Fear Effect

Abstract

This paper presents the formulation and investigation for a stage-structured prey-predator system. We consider the stage- structure in both prey and predator populations, specifically dividing the population of prey into two distinct groups: immature prey and mature prey. We also divide the predator population into immature and mature groups. We assume that only immature predators are capable of attack, so they consume each immature and mature prey. Additionally, the rate of growth for immature prey based on the amount of mature prey, as immature prey does not have reproductive capability. We applied Holling Type I and Holling Type IV response functions to describe the consumption of immature and mature prey by immature predators, respectively. We conducted a mathematical analysis: boundedness of the solution, the presence of equilibrium points, and both local and global stability of the proposed system with respect to these equilibrium points. We also performed numerical simulations to verify the theoretical results

Author Biographies

Bushra E. Kashem, Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Hassan F. Al-Husseiny, College of Applied Science, University of Technology, Baghdad, Iraq

Mathematics
Anwar Zeb, Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan

Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan.

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