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

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.