Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 290123, 16 pages
Research Article

Harvesting of a Single-Species System Incorporating Stage Structure and Toxicity

College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian, 350002, China

Received 25 June 2009; Accepted 8 November 2009

Academic Editor: Leonid Berezansky

Copyright © 2009 Huiling Wu and Fengde 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.


A single species stage-structured model incorporating both toxicant and harvesting is proposed and studied. It is shown that toxicant has no influence on the persistent property of the system. The existence of the bionomic equilibrium is also studied. After that, we consider the system with variable harvest effect; sufficient conditions are obtained for the global stability of bionomic equilibrium by constructing a suitable Lyapunov function. The optimal policy is also investigated by using Pontryagin's maximal principle. Some numeric simulations are carried out to illustrate the feasibility of the main results. We end this paper by a brief discussion.