DYNAMICS OF THE PREDATOR–PREY MODEL WITH PREY GROUP DEFENSE, ALTERNATIVE FOOD, AND PREDATOR ECOLOGICAL COSTS: STABILITY ANALYSIS AND NUMERICAL SIMULATION

Abstract

This study examines the dynamics of a predator-prey model that integrates three main biological mechanisms: the availability of alternative food for predators, group defense among prey, and the ecological cost in the form of additional predator mortality. Alternative food is modeled as an energy subsidy that affects the saturation level of interactions and biomass conversion efficiency, while group defense among prey represents the collective ability of prey to reduce predation success. The ecological cost is introduced as a consequence of increased predator dependence on additional resources. Analytically, it is proven that the system has solutions that exist, are unique, and remain within the relevant biological domain. Equilibrium point analysis shows the presence of both predator extinction and a stable interior of both populations, with stability determined by key model parameters. Numerical simulations verify the analytical results and clarify the biological interpretation, namely that enhancing the effectiveness of group defense among prey can lead to predator extinction, while a moderate amount of alternative food supports coexistence. However, excessive availability of alternative food accompanied by a high ecological cost can actually accelerate predator extinction. These results indicate that the interaction between external energy subsidies and prey defense mechanisms plays a crucial role in determining the long-term structural dynamics of ecosystems.