Boundary Value Problems
Volume 2008 (2008), Article ID 192353, 21 pages
doi:10.1155/2008/192353
Research Article

Global Behaviors and Optimal Harvesting of a Class of Impulsive Periodic Logistic Single-Species System with Continuous Periodic Control Strategy

JinRong Wang,1 X. Xiang,2 and W. Wei2

1College of Computer Science and Technology, Guizhou University, Guiyang, Guizhou 550025, China
2College of Science, Guizhou University, Guiyang, Guizhou 550025, China

Received 30 September 2008; Accepted 17 December 2008

Academic Editor: Wenming Zou

Copyright © 2008 JinRong Wang 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

Global behaviors and optimal harvesting of a class of impulsive periodic logistic single-species system with continuous periodic control strategy is investigated. Four new sufficient conditions that guarantee the exponential stability of the impulsive evolution operator introduced by us are given. By virtue of exponential stability of the impulsive evolution operator, we present the existence, uniqueness and global asymptotical stability of periodic solutions. Further, the existence result of periodic optimal controls for a Bolza problem is given. At last, an academic example is given for demonstration.