Role of Cooperative Hunting among Predators and Predator-Dependent Prey Refuge Behavior in a Predator-Prey Model (Journal of Nonlinear Modeling and Analysis, 2025)
The investigation of predator cooperative hunting and prey refugeis crucial for understanding ecological dynamics. In recent years, the roleof cooperative hunting or prey refuge in predator-prey systems has receivedmuch attention from researchers. However, the study on the combined effectsof predator cooperation and predator-dependent prey refuge in the predationsystem has not yet been investigated. Therefore, in this paper, we propose aprey-predator model with both the factors of predator-dependent prey refugeand cooperative hunting. The positivity and boundedness of the system’ssolutions are investigated, followed by the existence and local stability of theequilibrium points. Sufficient conditions for the existence of Hopf bifurcationof the system are obtained. The direction of Hopf bifurcation in the system isinvestigated by using the center manifold theorem and normal form method.From the analysis of the model, we find that the dependence coefficient $m$ ofthe prey refuge ratio on the number of predators may be responsible for thestability of the system. The results also indicate that suitable competitioncoefficients $s$ and cooperative hunting coefficients $α$ between predators mayenable the species to coexist in the long run. Furthermore, we observe two limitcycles of the system when the parameters satisfy certain conditions. Finally,the dynamical behavior of the model is performed through intriguing numericalsimulations.