Modelling and qualitative analysis of a predator–prey system with state-dependent impulsive effects

In this work, according to integrated pest management principles, a class of predator–prey system with state-dependent impulsive effects is put forward. In this model, the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered. The sufficient conditions for the existence and stability of the semi-trivial periodic solution and the positive order-1 periodic solution are given by the Poincaré map and the properties of the Lambert W function. In addition, to verify the feasibility of our main results, the numerical simulations are carried out.