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A Food Chain System with Density-Dependent Birth Rate and impulsive Perturbations

We investigate a three-species food chain system with density-dependent birth rate and impulsive effect concerning biological and chemical control strategy — periodic releasing of natural enemies or spraying pesticide at different fixed times. Conditions for the extinction of the prey and top predator are given. By using the Floquet theory of impulsive differential equations and small amplitude perturbation skills, we consider the local stability of the prey and top predator eradication periodic solution. Further, we obtain the conditions of permanence of the system.