Global dynamics for a non-smooth Filippov system with the threshold strategy

In this study, the Leslie-Gower model with functional response is extended into a non-smooth Filippov system by applying IPM strategies. Once the number of pests reaches or surpasses the given economic threshold(ET), spraying pesticides and releasing the natural enemy are implemented simultaneously. In order to maintain the pest population at or below ET, global dynamics of the proposed model are investigated completely, including the existence of sliding mode and various equilibria, sliding dynamics and global stability of equilibria. The result shows that real equilibrium cannot coexist with the unique pseudo-equilibrium. In particular, after excluding the existence of any possible limit cycle, the global stability of equilibria is obtained by employing qualitative and numerical techniques. In the end, the effect of our work on pest control are discussed.