Exploring fear effects in predator–prey systems across deterministic and stochastic frameworks

Abstract

This study examines the dynamics of a predator-prey model, highlighting the stabilizing influence of fear on prey and the resulting impacts on system stability and bifurcations. High fear levels in prey help stabilize predator-prey interactions by suppressing oscillations, while low fear levels tend to induce periodic oscillations through Hopf bifurcations. We explore both mono and bistability, as well as local and global stability, and analyze bifurcations, including transcritical and sub-/supercritical Hopf bifurcations. In addition, our investigation into stochastic stability shows that deterministic controls can effectively reduce environmental fluctuations when noise intensity is kept below a critical threshold. Numerical simulations reveal how fear, in conjunction with parameters like prey growth rate, predator abundance, and prey-predator conversion efficiency, can lead to limit cycles through Hopf bifurcation.