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Modeling and Analysis of Predator‐Prey Model with Fear Effect in Prey and Hunting Cooperation among Predators and Harvesting

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  • Basaznew Belew
  • Dawit Melese

Abstract

In this paper, we present and analyze predator‐prey system where prey population is linearly harvested and affected by fear and the prey population has grown logistically in the absence of predators. The predator population follows hunting cooperation, and it predates the prey population in the Holling type II functional responses. Based on those assumptions, a two‐dimensional mathematical model is derived. The positivity, boundedness, and extinction of both prey and predator populations of the solution of the system are discussed. The existence, stability (local and global), and the Hopf bifurcation analysis of the biologically feasible equilibrium points are investigated. The aim of this research is to explore the effect of fear on the prey population and hunting cooperation on the predator population, and both prey and predator populations are harvested linearly and taken as control parameters of the model. If the values of c1 > 1, then both prey and predator populations are extinct and also fear parameter has a stabilizing effect on system 4. From the numerical simulation, it was found that the fear effect, hunting cooperation, prey harvesting, and predator harvesting change the dynamics of system 4.

Suggested Citation

  • Basaznew Belew & Dawit Melese, 2022. "Modeling and Analysis of Predator‐Prey Model with Fear Effect in Prey and Hunting Cooperation among Predators and Harvesting," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnljam:v:2022:y:2022:i:1:n:2776698
    DOI: 10.1155/2022/2776698
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    1. Jialin Chen & Xiaqing He & Fengde Chen, 2021. "The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
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    Cited by:

    1. Rasha Ali Hamodi & Karrar Qahtan Al-Jubouri & Reem Mudar Hussien & Raid Kamel Naji, 2025. "The Dynamical Analysis of Food‐Web System With a Group Defense and Antipredator Property," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    2. Basaznew Belew, 2025. "Analyzing the Effect of Fear, and Refuge on Prey, Harvesting, and Hunting Cooperation Among Predators on Leslie–Gower Predator Prey Model," International Journal of Differential Equations, John Wiley & Sons, vol. 2025(1).
    3. Hersh Aziz Mohammed & Arkan Nawzad Mustafa, 2025. "Dynamical Analysis of a Delay Two‐Prey–One‐Predator Model Incorporating Fear Effect in the Growth Rate of Preys," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).

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