Journal of Applied Mathematics
Volume 2012 (2012), Article ID 794719, 15 pages
http://dx.doi.org/10.1155/2012/794719
Research Article

A Dynamic Model for Fishery Resource with Reserve Area and Taxation

Hai-Feng Huo,1 Hui-Min Jiang,1,2 and Xin-You Meng1

1Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
2Department of Mathematics, School of Science, Shihezi University, Shihezi, Xinjiang 832003, China

Received 13 June 2011; Revised 5 October 2011; Accepted 6 October 2011

Academic Editor: Meng Fan

Copyright © 2012 Hai-Feng Huo 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.

Abstract

The present paper deals with a dynamic reaction model of a fishery. The dynamics of a fishery resource system in an aquatic environment consists of two zones: a free fishing zone and a reserve zone. To protect fish population from over exploitation, a control instrument tax is imposed. The existence of its steady states and their stability are studied. The optimal harvest policy is discussed next with the help of Pontryagin's maximum principle. Our theoretical results are confirmed by numerical simulation.