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Extinction and permanence of a kind of pest-predator models with impulsive effect and infinite delay. (English) Zbl 1143.34052

Summary: A kind of pest-predator model with impulsive effect and infinite delay is considered. By using Floquet’s theorem, it is shown that there exists a globally asymptotically stable periodic pest eradication solution when the impulsive period is less than or equal to some critical value which is a directly proportional function with respect to the population of release. Furthermore, it is proved that the system is permanent if the impulsive period is larger than some threshold value. Finally, the results of the corresponding systems are confirmed by numerical simulations.

MSC:

34K45 Functional-differential equations with impulses
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