Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 86482, 15 pages
doi:10.1155/2007/86482
Research Article
Harvesting Control for a Stage-Structured Predator-Prey Model with Ivlev's Functional Response and Impulsive Stocking on Prey
1Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China
2Department of Mathematics, Anshan Normal University, Anshan 114007, China
Received 8 July 2007; Accepted 17 October 2007
Copyright © 2007 Kaiyuan Liu and Lansun Chen. 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
We investigate a delayed stage-structured Ivlev's functional response predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained. These results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactical basis for the biological resource management and enrich the theory of impulsive delay differential equations.