A discrete predator-prey model with prey logistic growth and cooperative hunting among predators

Based on research on a predator-prey model with cooperative hunting and different prey growth rates, this paper examines a discrete predator-prey model with cooperative hunting in predator populations and logistic prey growth rate where the prey population does not move in the group. The study investigates various ecological equilibria of the model, including extinction, predator-free equilibrium, and coexisting equilibria. It delves into the local behavior of populations at these equilibrium states and provides global results for extinction and predator-free conditions. The study proves transcritical, period-doubling, and Neimark-Sacker bifurcation occurence. It also proves uniform persistence under specific conditions and parameters when there is instability in predator-free equilibrium. Numerical simulations reveal complex dynamic behavior, especially for specific parameter values. Finally, the study compares its results with previous research on similar topics.