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Dynamic behaviors of the periodic predator-prey model with modified Leslie-Gower Holling-type II schemes and impulsive effect. (English) Zbl 1142.34031
The authors investigate a T-periodic predator-prey model with modified Leslie-Gower and Holling-type II terms which, moreover, is governed by periodically placed impulses. They first derive results on existence and uniquness of a positive periodic solution for one of the two species if the second one vanishes. Then, using Floquet theory for linear periodic impulsive equations, the authors establish local stability conditions for the above-mentioned solutions, and finally, applying the bifurcation theorem of Rabinowitz to these solutions, they prove a result on the existence of a strictly positive periodic solution for both species. An example concludes the paper.

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
92D25 Population dynamics (general)
34A37 Ordinary differential equations with impulses
34C23 Bifurcation theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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