Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 290123, 16 pages
doi:10.1155/2009/290123

Harvesting of a single-species system incorporating stage structure and toxicity

Abstract

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.