The dynamics of pest control pollution model with age structure and time delay. (English) Zbl 1191.92074

Summary: By using a pollution model and impulsive delay differential equations, we investigate the dynamics of a pest control model with age structure for pest by introducing a constant periodic pesticide input and releasing natural enemies at different fixed moment. We assume only the pests are affected by pesticides. We show that there exists a global attractive pest-extinction periodic solution when the periodic natural enemies release amount \(\mu _{1}\) and pesticide input amount \(\mu _{2}\) are larger than some critical value. Further, a condition for the permanence of the system is also given. By numerical analyses, we also show that constant maturation time delay, pulse pesticide input and pulse releasing of the natural enemies can bring obvious effects on the dynamics of system. We believe that the results will provide reliable tactic basis for the practical pest management.


92D40 Ecology
34K45 Functional-differential equations with impulses
34K13 Periodic solutions to functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
Full Text: DOI


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