Predator-Prey Interaction Model with Hunting Cooperation among Predators and Allee Effect in Prey

TL;DR

This paper models predator-prey dynamics incorporating hunting cooperation among predators and the Allee effect in prey, analyzing stability and demonstrating how cooperation influences population outcomes through numerical simulations.

Contribution

It introduces a novel predator-prey model with hunting cooperation and Allee effect, analyzing stability and population dynamics with numerical verification.

Findings

Hunting cooperation can switch the stability of coexistence equilibrium.

Increasing hunting cooperation may lead to extinction of both species.

The model's stability depends on the level of hunting cooperation.

Abstract

This paper investigates a dynamical predator-prey interaction model that incorporates: (a) hunting cooperation among predators; (b) Allee effect in prey. We show all possible boundary and interior solutions. In order to analyze the stability of the solution, we make use of the Jacobian matrix and the resultant characteristic polynomial. Particularly, the sign of the eigenvalue is used to determine the stability of a solution. We then provide proof for stability of the interior solution. Finally, we verify our results numerically in MATLAB by plotting: (1) predator-prey intersection graphs; (2) prey-predator vs hunting cooperation graphs; (3) initial condition trajectory for equilibrium solution. It is interesting to notice that hunting cooperation can switch the stability of coexistence equilibrium solutions. Through numerical simulations, it was verified that increasing the hunting cooperation could lead to the extinction of both prey and predator population for alpha greater than 0.96, given our choice of parameters.