A food chain system with Holling type IV functional response and impulsive perturbations

In this paper, 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 a...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2010-09, Vol.60 (5), p.1152-1163
Main Author: Baek, Hunki
Format: Article
Language:English
Subjects:
A food chain system
Computer simulation
Floquet theory
Food chain
Holling type IV functional response
Impulsive differential equation
Mathematical analysis
Mathematical models
Perturbation methods
Skills
Stability
The comparison theorem
Theorems
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Summary:In this paper, 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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2010.05.039