Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 181752, 21 pages
Research Article

Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model

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

Received 18 February 2012; Accepted 10 April 2012

Academic Editor: Recai Kilic

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.


According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one periodic solution of such system and the attractiveness 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 and easier than the existing ones for proving the existence of order one periodic solution.