Modeling and Analysis of the Influence of Fear on the Harvested Modified Leslie–Gower Model Involving Nonlinear Prey Refuge

Abdul Rahman Mahmoud Jamil and Raid Kamel Naji ()
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Abdul Rahman Mahmoud Jamil: Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq
Raid Kamel Naji: Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq

Mathematics, 2022, vol. 10, issue 16, 1-22

Abstract: Understanding the effects of fear, quadratic fixed effort harvesting, and predator-dependent refuge are essential topics in ecology. Accordingly, a modified Leslie–Gower prey–predator model incorporating these biological factors is mathematically modeled using the Beddington–DeAngelis type of functional response to describe the predation processes. The model’s qualitative features are investigated, including local equilibria stability, permanence, and global stability. Bifurcation analysis is carried out on the temporal model to identify local bifurcations such as transcritical, saddle-node, and Hopf bifurcation. A comprehensive numerical inquiry is carried out using MATLAB to verify the obtained theoretical findings and understand the effects of varying the system’s parameters on their dynamical behavior. It is observed that the existence of these factors makes the system’s dynamic behavior richer, so that it involves bi-stable behavior.

Keywords: fear; predator-dependent refuge; quadratic fixed effort harvesting; Leslie–Gower prey–predator model; stability; bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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