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

TL;DR

This paper analyzes a predator-prey model incorporating prey herd behavior, mutual interference, and fear effects, revealing how fear can lead to prey extinction or stabilize coexistence, with implications for ecological management.

Contribution

It introduces a comprehensive analysis of a predator-prey model with fear and herd behavior, providing bifurcation conditions and exploring the impact of harvesting on system stability.

Findings

Fear can cause prey extinction in finite time.

Varying fear strength can stabilize or destabilize coexistence.

Harvesting can shift dynamics from extinction to stable coexistence.

Abstract

A deterministic two-species predator-prey model with prey herd behavior is considered incorporating mutual interference and the effect of fear. We provide guidelines to the dynamical analysis of biologically feasible equilibrium points. 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. Additionally, 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. Furthermore, we perform extensive numerical experiments to visualize the dynamical behavior of the model and substantiate the results we obtained.