The geometrical analysis of a predator–prey model with two state impulses

Using successor functions and Poincaré–Bendixson theorem of impulsive differential equations, the existence of periodical solutions to a predator–prey model with two state impulses is investigated. By stability theorem of periodic solution to impulsive differential equations, the stability conditions of periodic solutions to the system are given. Some simulations are exerted to prove the results.

► A prey-predator model with two state impulses is proposed.
► In a view of geometry, successor functions are applied to analyze the model.
► The existence of periodical solutions to the model is discussed completely.
► An algorithm and numerical simulations are given to verify our conclusions.