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A food chain system with Holling type IV functional response and impulsive perturbations. (English) Zbl 1201.34015
Summary: A three-trophic-level food chain system with Holling type IV functional response and impulsive perturbations is established. We show that this system is uniformly bounded. Using the Floquet theory of impulsive equations and small perturbation skills, we find conditions for the local and global stabilities of the prey and top predator-free periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent via the comparison theorem. We display some numerical examples to substantiate our theoretical results.
MSC:
34A37Differential equations with impulses
34C25Periodic solutions of ODE
34D20Stability of ODE
92D25Population dynamics (general)
37N25Dynamical systems in biology
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