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The dynamics of a high-dimensional delayed pest management model with impulsive pesticide input and harvesting prey at different fixed moments. (English) Zbl 1280.34078

Summary: In this paper, a delayed pest control model with stage-structure for pests by introducing a constant periodic pesticide input and harvesting prey (Crops) at two different fixed moments is proposed and analyzed. We assume only the pests are affected by pesticide. We prove that the conditions for global asymptotically attractive ‘predator-extinction’ periodic solution and permanence of the population of the model depend on time delay, pulse pesticide input, and pulse harvesting prey. By numerical analysis, we also show that constant maturation time delay, pulse pesticide input, and pulse harvesting prey can bring obvious effects on the dynamics of system, which also corroborates our theoretical results. We believe that the results will provide reliable tactic basis for the practical pest management. One of the features of present paper is to investigate the high-dimensional delayed system with impulsive effects at different fixed impulsive moments.

MSC:

34K45 Functional-differential equations with impulses
92D25 Population dynamics (general)
34K13 Periodic solutions to functional-differential equations
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