## The geometrical analysis of a predator-prey model with two state impulses.(English)Zbl 1250.92047

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

### MSC:

 92D40 Ecology 34A37 Ordinary differential equations with impulses 34C25 Periodic solutions to ordinary differential equations 37N25 Dynamical systems in biology 65C20 Probabilistic models, generic numerical methods in probability and statistics
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### References:

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