Predator-prey system with a boundary-upstream protection zone in open advective environments

In river ecosystems, unidirectional flow and habitat fragmentation threaten prey persistence, necessitating protection zones. This study explores the dynamics of a generalist predator-prey model with a boundary-upstream protection zone for prey and Holling-II type functional response in open advective environments. Firstly, we establish complete system dynamics driven by the interplay of variable advection rates, protection zone lengths and predator carrying capacity, revealing their coupled effects on population persistence and extinction. We identify a critical protection zone length, beyond which predator take-over is prevented within a prey advection range, regardless of predator strength, thereby promoting species coexistence. Furthermore, through bifurcation analysis, the existence and multiplicity for positive steady states are studied, linking prey attack-evasion ability and predator advection rate to bistable outcomes. The asymptotic behaviors of positive steady states induced by large diffusion rates are characterized, showing that enhanced dispersal counteracts flow-induced washout. This study uniquely integrates Holling-II response with upstream refuge effects, revealing critical thresholds for predator control. The findings guide designing flow-adaptive protection zones to mitigate generalist predator dominance in aquatic ecosystems, offering actionable management strategies.