Existence of positive periodic solution of generalized Gilpin–Ayala competition systems with discontinuous harvesting policies

Considering the impact of discontinuous harvesting policy (DHP) on dynamics of Gilpin–Ayala competition systems, the following n-species generalized Gilpin–Ayala competition system with time delays and DHP is proposed.dxitdt=xitbit−∑j=1n∫0∞xjθijtt−sdsKijts−εithixitxit,i=1,2,…,n.By differential inclusion theory and cone expansion and compression fixed point theorem of multi-valued maps, some sufficient conditions of existence of positive periodic solutions are established for the generalized Gilpin–Ayala competition system with discontinuous harvesting policies. The results of references are improved and extended.MSC: 34K13.