Boundary Value Problems
Volume 2008 (2008), Article ID 192353, 21 pages
doi:10.1155/2008/192353
Global behaviors and optimal harvesting of a class of impulsive periodic logistic single-species system with continuous periodic control strategy
Jinrong Wang1
, X. Xiang2
and W. Wei2
1College of Computer Science and Technology, Guizhou University, Guiyang, Guizhou 550025, China
2College of Science, Guizhou University, Guiyang, Guizhou 550025, China
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.