Effect of advection on the predator-prey dynamics with a drift-feeding predator

We examine a diffusive predator-prey model with a drift-feeding predator in open advective environments. Our analysis reveals key insights: (i) When predator mortality is low, the stability of the semi-trivial steady state can shift at least twice as flow speed increases, regardless of predator diffusion; (ii) For intermediate mortality and low diffusion, stability transitions occur, but beyond a critical diffusion threshold, the steady state remains stable regardless of flow speed. Using bifurcation theory and auxiliary methods, we establish the existence and uniqueness of a positive steady state. Unlike previous studies suggesting increased flow speed harms population persistence, our results show it can sometimes promote predator-prey coexistence, highlighting the complex effects of advection on ecological dynamics.