In　this　paper,　a　patchy　model　in　which　the　migration　is　induced　by　the　fear　effect　on　the　predator　was　investigated.　By　applying　dynamical　theory,　the　complete　study　on　persistence　of　the　system　and　the　local/global　stability　of　equilibria　were　discussed.　Choosing　the　diffusion　coefficient　D1　as　the　bifurcation　parameter,　transcritical　bifurcation　occurring　near　the　trivial　equilibrium　was　demonstrated.　We　concluded　that　low　dispersal　is　favorable　for　the　coexistence　of　both　species,　but　large　dispersal　leads　to　the　extinction　of　species.　There　is　an　optimal　diffusion　coefficient　to　make　the　density　of　the　prey　population　reach　its　maximum.　In　addition,　the　level　of　fear　effect　k　and　the　maximum　fear　cost　η　are　beneficial　to　the　total　population　density　of　prey.　©　2025　the　Author(s)