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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 936024, 10 pages
http://dx.doi.org/10.1155/2012/936024
Research Article

Optimal Management during the Microorganism Culture Based on the Continuous Purifying Effort

Junior College, Zhejiang Wanli University, Zhejiang, Ningbo 315100, China

Received 30 July 2012; Accepted 25 October 2012

Academic Editor: Beatrice Paternoster

Copyright © 2012 Xianbin Wu. 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

This paper deals with the problem of selective harvesting in a chemostat model. Here, we have taken the purifying effort as a dynamic variable and tax as a control instrument. The existence of the possible steady states along with their globally stable equilibrium is discussed. The optimal tax policy is also discussed with the help of Pontryagin's maximum principle. Finally, numerical examples are taken to illustrate some of the key results.