In　this　paper,　we　investigate　a　Holling-Tanner　predator–prey　model　with　harvesting　and　anti-predator　behavior.　It　is　shown　that　the　double　positive　equilibrium　is　a　cusp　of　codimension　2,　the　triple　positive　equilibrium　is　a　nilpotent　saddle　of　codimension　3,　and　the　order　of　weak　focus　is　3.　With　influence　of　harvesting　and　anti-predator　behavior,　system　exhibits　complex　bifurcation　phenomena　such　as　a　cusp　type　Bogdanov–Takens　bifurcation　of　codimension　2,　and　a　degenerate　Hopf　bifurcation　of　codimension　3.　©　2025　Elsevier　Ltd