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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:
 34A37 Differential equations with impulses 34C25 Periodic solutions of ODE 34D20 Stability of ODE 92D25 Population dynamics (general) 37N25 Dynamical systems in biology
##### References:
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