Dynamic Behavior Analysis For Multi-population Predator-prey System With Discontinuous Harvesting Policy

In this paper,we study a three-species predator-prey system with discontinuous harvesting policies,in which three populations are composed of two predators and one prey.First of all,in order to study the dynamic behavior of the system under the framework of Filippov theory,the ternary block continuous function is adopted to define the discontinuous harvesting function.For this three-species predator-prey system with multiple discontinuous harvesting policies,we consider Hassell-Varley type and Beddington-De Angelis type functional response functions with mutual interference,respectively.Firstly,the local existence,global existence and uniform persistence of the positive solution are studied respectively in the sense of Filippov solution when the interaction constants m?(0,1)and m?(0,1)of the system are respectively studied.Second,when a system of interacting constant for m?(0,1)and m =1 for interacting constant,applied to the right end functional differential equations with discontinuous differential theory,the topological degree theory of set-valued analysis,respectively,for the mutual interference of the system are given with the constant m?(0,1)and m =1 for interacting constant corresponding sufficient conditions for the existence of periodic solutions for periodic systems,necessary condition and there is no relevant results.Finally,some related numerical examples are given to illustrate the existence and nonexistence of periodic solutions of the system.