EXISTENCE AND ASYMPTOTIC BEHAVIOR OF COEXISTENCE STATES TO A DIFFUSIVE HOLLING TYPE II PREDATOR-PREY MODEL WITH HUNTING COOPERATION

In this paper, we delve into a diffusive Holling type II predator-prey model, incorporating the element of hunting cooperation, and examine it under Dirichlet boundary conditions. Our primary focus is on addressing two pivotal questions: Firstly, we endeavor to establish the existence of coexistence states across a range of hunting cooperation effects. This exploration aims to reveal how the predator and prey species can maintain their coexistence within the ecological system, regardless of the magnitude of cooperation among predators during hunting. Secondly, we are interested in elucidating the asymptotic behavior of these coexistence states as the cooperation parameter approaches infinity. This analysis will provide insights into how the ecological balance shifts as the predators' cooperation increases indefinitely, offering a deeper understanding of the long-term ecological implications of such cooperation.