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Modelling and analysis of integrated pest management strategy. (English) Zbl 1114.92074

Summary: Two impulsive models concerning integrated pest management (IPM) are proposed according to impulsive effects with fixed moments and unfixed moments, respectively. The first model has the potential to protect the natural enemies from extinction, but under some conditions may also serve to extinction of the pest. The second model is constructed according to the practices of IPM, that is, when the pest population reaching the economic injury level, a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is used. By using analytical methods, we show that there exists an orbitally asymptotically stable periodic solution with a maximum value no larger than the given economic threshold. Further, the complete expression of the period of the periodic solution is given. Thus, the IPM strategy proved firstly by mathematical models is more effective than the classical method.

MSC:

92D40 Ecology
34A37 Ordinary differential equations with impulses
34C25 Periodic solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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