Modeling and analysis of impulsive dispersal of fear effect and hunting cooperation of predator on prey in patchy habitat

The complex interaction between cooperative hunting strategies among predators and the resulting fear-induced responses in prey has become an increasingly important focus in ecological research. This study presents a comprehensive prey-predator model to explore these dynamics within a two-patch environment, where prey can move between patches impulsively. In contrast, predators are confined to a single patch and are structured into two developmental stages: immature and mature, with only the mature individuals actively hunting prey. Utilizing the theory of impulsive differential equations, we establish the existence of a globally attractive predator-free periodic solution under specific timing conditions for the impulsive prey movement. To assess the potential for long-term species coexistence, we employ comparison theorems tailored to impulsive systems to demonstrate the model’s permanence. A key result reveals that the delay in predator maturation plays a crucial role in determining whether populations persist or go extinct. Numerical simulations are provided to validate and illustrate the theoretical outcomes.