Fear-driven gregariousness and survival: Modeling bidirectional feedbacks and seasonality in a generalist predator–prey system

Prey fear and gregarious behavior form a bidirectional feedback loop critical to ecosystem stability. We quantify this bidirectional feedback by using GSE mechanisms and extending this framework to seasonal environments. Mathematical analysis and numerical simulations validate the proposed model. Research shows that increasing fear intensity eliminates positive equilibria via saddle–node bifurcation, while GSE mitigates this by enhancing group survival. Under bistability, the number, spatial distribution, and stability of interior equilibria exhibit selective dependence on both fear parameter and GSE. Fear and GSE form a feedback loop that can stabilize ecosystems or trigger extinction via bistability. Notably, fear effects and GSE exert opposing influences on model dynamics. Furthermore, it is highlighted that seasonal variations modulate but do not fundamentally alter the underlying stability structure dictated by fear and group size effect. Seasonal forcing amplifies these dynamics, with prey initial density being critical to persistence. This study establishes the first theoretical framework unifying GSE-driven fear feedbacks and seasonal forcing, offering mechanistic insights into ecosystem resilience and extinction thresholds.