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An impulsive predator-prey system with modified Leslie-Gower and Holling type II schemes. (English) Zbl 1148.34034
Summary: An impulsive predator-prey system with modified Leslie-Gower and Holling-type II schemes is presented. By using the Floquet theory of impulsive equation and the small amplitude perturbation method, the global asymptotical stability of a prey-free positive periodic solution and the permanence of the system are discussed. The corresponding threshold conditions are obtained respectively. Finally, numerical simulations are given.

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
92D25 Population dynamics (general)
34D05 Asymptotic properties of solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34A37 Ordinary differential equations with impulses
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