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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 126018, 18 pages
http://dx.doi.org/10.1155/2012/126018
Research Article

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

College of Science, Shandong University of Science and Technology, Qingdao 266510, China

Received 16 April 2012; Accepted 13 August 2012

Academic Editor: Narcisa C. Apreutesei

Copyright © 2012 Huidong Cheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.