Bioeconomic Perspectives on Sustainable Harvesting in Predator–Prey System with Defensive Prey and Generalist Predator

This study proposes a bioeconomic predator–prey model that explores the interaction between a generalist predator and a defensive prey species under nonlinear predation and independent harvesting. The model is designed with sustainability in mind, aiming to identify conditions that promote long-term coexistence, prevent extinction, and maintain ecological and economic balance. Predator–prey dynamics are governed by a Holling-Type IV functional response, which reflects reduced predation efficiency at high prey densities due to group defense mechanisms. The model extends existing frameworks by incorporating logistic growth for both species, intraspecific competition for both the prey and predator populations, and adaptive predator foraging behavior. We perform a comprehensive mathematical analysis, establishing boundedness and the existence of biologically feasible equilibria. We analyze the local stability of equilibria using the Routh–Hurwitz criterion, and assess global stability using Lyapunov functions. In addition, we investigate the conditions for the existence of bionomic equilibrium and explore the emergence of limit cycles through the numerical calculation of the first Lyapunov coefficient. Numerical simulations are given to illustrate rich dynamical patterns, including stable coexistence, extinction scenarios, and oscillatory regimes. The ecological aspects, along with the behavioral adaptations of the populations, are highlighted.