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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:
34C60Qualitative investigation and simulation of models (ODE)
92D25Population dynamics (general)
34A37Differential equations with impulses
34C23Bifurcation (ODE)
34C25Periodic solutions of ODE