By　incorporating　the　density　dependent　birth　rate　to　the　traditional　May　type　cooperative　system,　we　propose　the　following　cooperative　system　(Formula　presented)　are　all　positive　constants.　By　applying　the　comparison　principle,　sufficient　conditions　which　ensure　the　extinction,　partial　survival　and　permanence　of　the　system　are　obtained,　respectively.　By　applying　the　Dulac　criterion,　a　set　of　sufficient　conditions　which　ensure　the　existence　of　a　unique　globally　asymptotically　stable　equilibrium　is　obtained.　Numeric　simulations　are　carried　out　to　show　the　feasibility　of　the　main　results.　©　2020,　International　Association　of　Engineers.　All　rights　reserved.