Existence and stability of periodic solution of a Lotka–Volterra predator–prey model with state dependent impulsive effects

According to biological and chemical control strategy for pest, we investigate the dynamic behavior of a Lotka–Volterra predator–prey state-dependent impulsive system by releasing natural enemies and spraying pesticide at different thresholds. By using Poincaré map and the properties of the Lambert W function, we prove that the sufficient conditions for the existence and stability of semi-trivial solution and positive periodic solution. Numerical simulations are carried out to illustrate the feasibility of our main results.