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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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