Existence and stability of periodic solution of a predator-prey model with state-dependent impulsive effects

According to integrated pest management for pests, we investigate the dynamic behavior of a class predator-prey system with state-dependent impulsive effects by releasing natural enemies and spraying pesticide at different thresholds. Using the Poincare map and the properties of the Lambert W function, we prove the sufficient conditions for the existence and stability of semi-trivial solutions and positive periodic solutions. Numerical results are carried out to illustrate the feasibility of our main results.

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