Existence and Attractiveness of Order One Periodic Solution of a Holling I Predator-Prey Model

According to the integrated pest management strategies, a Holling type I functional response predator-prey system concerning state-dependent impulsive control is investigated. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one pe...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2012-01, Vol.2012 (2012), p.327-344
Main Authors: Cheng, Huidong, Wang, Fang, Zhang, Tongqian
Format: Article
Language:English
Subjects:
Convergence (Mathematics)
Existence theorems
Mathematical models
Periodic functions
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Summary:According to the integrated pest management strategies, a Holling type I functional response predator-prey system concerning state-dependent impulsive control is investigated. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution, and the attractivity of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient than the existing ones for proving the existence and attractiveness of order one periodic solution.
ISSN:1085-3375
1687-0409
DOI:10.1155/2012/126018