Stabilizing predator-prey interactions: the impact of supplementary food and anti-predator behavior

This study investigated a modified Holling-Tanner predator-prey model that incorporates supplementary food for predators and anti-predator behavior in prey. The model examined how these ecological mechanisms influence predator-prey dynamics and biological pest control. Local and global stability analyses were performed to determine the conditions that lead to predator persistence and pest eradication. Explicit parametric conditions were derived that guarantee global pest extinction, providing quantitative criteria for effective biological control. Bifurcation analysis revealed the presence of Hopf and saddle-node bifurcations, which identify critical parameter thresholds where the system transitions between stable equilibria, oscillatory dynamics, and collapse of coexistence states. The results showed that anti-predator behavior can stabilize population dynamics and suppress oscillatory behavior that would otherwise occur in the absence of prey defense mechanisms. A reaction-diffusion extension of the model was then considered to investigate spatial effects. Turing instability analysis demonstrated that the interaction between diffusion and anti-predator behavior can generate persistent spatial patterns, offering a mechanistic explanation for patchy predator distributions frequently observed in agricultural ecosystems. The analysis further indicated that the effectiveness of biological control depends on the balance between supplementary food quantity, predation pressure, and the strength of prey defense. Excessive food supplementation may reduce predator pressure on pests and weaken pest suppression. Numerical simulations supported the analytical results and illustrated parameter regimes that lead to system stabilization and successful pest management. The proposed framework provides theoretical guidance for designing predator-based biological control strategies that combine resource provisioning with natural behavioral responses.