Fear-driven extinction and (de)stabilization in a predator-prey model incorporating prey herd behavior and mutual interference

Kwadwo Antwi-Fordjour; Rana D. Parshad; Hannah E. Thompson; Stephanie B. Westaway; Kwadwo Antwi-Fordjour; Rana D. Parshad; Hannah E. Thompson; Stephanie B. Westaway

doi:10.3934/math.2023173

AIMS Mathematics

2023, Volume 8, Issue 2: 3353-3377. doi: 10.3934/math.2023173

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Research article

Fear-driven extinction and (de)stabilization in a predator-prey model incorporating prey herd behavior and mutual interference

1.
Department of Mathematics and Computer Science, Samford University, Birmingham, AL 35229, USA
2.
Department of Mathematics, Iowa State University, Ames, IA 50011, USA
3.
Department of Biological and Environmental Sciences, Samford University, Birmingham, AL 35229, USA

Received: 03 October 2022 Revised: 13 November 2022 Accepted: 15 November 2022 Published: 17 November 2022
MSC : 34D35, 37C75, 37G15, 92B05

The indirect effect of predation due to fear has proven to have adverse effects on the reproductive rate of the prey population. Here, we present a deterministic two-species predator-prey model with prey herd behavior, mutual interference, and the effect of fear. We give conditions for the existence of some local and global bifurcations at the coexistence equilibrium. We also show that fear can induce extinction of the prey population from a coexistence zone in finite time. Our numerical simulations reveal that varying the strength of fear of predators with suitable choice of parameters can stabilize and destabilize the coexistence equilibrium solutions of the model. Further, we discuss the outcome of introducing a constant harvesting effort to the predator population in terms of changing the dynamics of the system, in particular, from finite time extinction to stable coexistence.
- fear effect,
- finite time extinction,
- prey herd behavior,
- mutual interference,
- harvesting
Citation: Kwadwo Antwi-Fordjour, Rana D. Parshad, Hannah E. Thompson, Stephanie B. Westaway. Fear-driven extinction and (de)stabilization in a predator-prey model incorporating prey herd behavior and mutual interference[J]. AIMS Mathematics, 2023, 8(2): 3353-3377. doi: 10.3934/math.2023173

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Abstract

The indirect effect of predation due to fear has proven to have adverse effects on the reproductive rate of the prey population. Here, we present a deterministic two-species predator-prey model with prey herd behavior, mutual interference, and the effect of fear. We give conditions for the existence of some local and global bifurcations at the coexistence equilibrium. We also show that fear can induce extinction of the prey population from a coexistence zone in finite time. Our numerical simulations reveal that varying the strength of fear of predators with suitable choice of parameters can stabilize and destabilize the coexistence equilibrium solutions of the model. Further, we discuss the outcome of introducing a constant harvesting effort to the predator population in terms of changing the dynamics of the system, in particular, from finite time extinction to stable coexistence.

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