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The dynamics of a mutual interference age structured predator-prey model with time delay and impulsive perturbations on predators. (English) Zbl 1184.92059
Summary: We introduce a mutual interference age structured predator-prey (natural enemy-pest) model with constant maturation time delay for the prey, and then propose a pest management strategy by constant periodic releasing for the predator. We show that there exists a global attractive pest-eradication periodic solution when the periodic releasing amounts μ 1 and μ 2 are lager than some critical value. Further, to obtain a more effective pest control strategy, we give conditions (involving the estimate of μ 1 and μ 2 ) under which the model is uniformly permanent and the pest population is under an economic threshold level. We believe that the results will provide reliable tactic basis for the practical pest management.
MSC:
92D40Ecology
34K60Qualitative investigation and simulation of models
34K35Functional-differential equations connected with control problems
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