Boundary Value Problems
Volume 2008 (2008), Article ID 192353, 21 pages
Global Behaviors and Optimal Harvesting of a Class of Impulsive Periodic Logistic Single-Species System with Continuous Periodic Control Strategy
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.
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.