We　propose　a　class　of　amensalism　population　models　in　which　the　refuge　is　related　to　the　density　of　the　second　population.　For　the　autonomous　case,　we　obtain　precise　thresholds　that　guarantee　the　extinction　or　stable　survival　of　the　first　population.　For　the　non-autonomous　case,　sufficient　conditions　are　obtained　to　ensure　the　system’s　persistence,　global　asymptotical　stability,　and　extinction,　respectively.　We　demonstrate　the　feasibility　of　the　main　results　with　the　help　of　numerical　simulations.　©　2024,　International　Association　of　Engineers.　All　rights　reserved.