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The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear

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  • Firas Hussean Maghool
  • Raid Kamel Naji

Abstract

The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels. It is assumed that the generalist predator grows logistically using the Leslie-Gower type of growth function. All the solution properties of the model are studied. Local dynamics behaviors are investigated. The basin of attraction for each equilibrium is determined using the Lyapunov function. The conditions of persistence of the model are specified. The study of local bifurcation in the model is done. Numerical simulations are implemented to show the obtained results. It is watched that the system is wealthy in its dynamics including chaos. The fear factor works as a stabilizing factor in the system up to a specific level; otherwise, it leads to the extinction of the predator. However, increasing the prey’s group defense leads to extinction in predator species.

Suggested Citation

  • Firas Hussean Maghool & Raid Kamel Naji, 2021. "The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-21, September.
  • Handle: RePEc:hin:jnljam:2112814
    DOI: 10.1155/2021/2112814
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    Cited by:

    1. Abdul Rahman Mahmoud Jamil & Raid Kamel Naji, 2022. "Modeling and Analysis of the Influence of Fear on the Harvested Modified Leslie–Gower Model Involving Nonlinear Prey Refuge," Mathematics, MDPI, vol. 10(16), pages 1-22, August.
    2. Zainab Saeed Abbas & Raid Kamel Naji, 2022. "Modeling and Analysis of the Influence of Fear on a Harvested Food Web System," Mathematics, MDPI, vol. 10(18), pages 1-37, September.
    3. Hiba Abdullah Ibrahim & Raid Kamel Naji, 2023. "The Impact of Fear on a Harvested Prey–Predator System with Disease in a Prey," Mathematics, MDPI, vol. 11(13), pages 1-28, June.

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