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Qualitative analysis of a modified Leslie-Gower and Holling-type II predator-prey model with state dependent impulsive effects. (English) Zbl 1228.37058
Summary: We present a two-dimensional autonomous dynamical system modeling a predator-prey food chain which is based on a modified version of the Leslie-Gower scheme and on the Holling-type II scheme with state dependent impulsive effects. By using the Poincaré map, some conditions for the existence and stability of a semi-trivial solution and a positive periodic solution are obtained. Numerical results are carried out to illustrate the feasibility of our main results.

MSC:
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
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