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Dynamic analysis of an impulsive predator-prey model with disease in prey and Ivlev-type functional response. (English) Zbl 1246.92028
Summary: A predator-prey model with disease in the prey, Ivlev-type functional response, and impulsive effects is proposed. By using Floquet theory and small amplitude perturbations skill, sufficient conditions for existence and global stability of susceptible pest-eradication periodic solutions are obtained. By the impulsive comparison theorem, conditions ensuring the permanence of the system are established. Examples and simulations are given to show the complex dynamics of the key parameters.

MSC:
92D40 Ecology
37N25 Dynamical systems in biology
34A37 Ordinary differential equations with impulses
65C20 Probabilistic models, generic numerical methods in probability and statistics
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