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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 3925386, 7 pages
http://dx.doi.org/10.1155/2016/3925386
Research Article

The Modelling and Control of a Singular Biological Economic System in a Polluted Environment

1School of Science, Shenyang University of Technology, Shenyang 110870, China
2School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
3State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China
4School of Science, Lanzhou University of Technology, Lanzhou 730050, China

Received 1 November 2015; Accepted 29 February 2016

Academic Editor: Viktor Avrutin

Copyright © 2016 Yi Zhang 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

A singular biological economic model with harvesting and stage structure is presented. The local stability of equilibriums of the system is investigated when the economic profit parameter is zero, and the conditions of the singularity induced bifurcation occurring at the positive equilibrium are obtained by the singular systems theory and bifurcation theory. In order to eliminate the singularity induced bifurcation, a state feedback controller is designed by controlling the fishing effort. At last, an application example is given to illustrate the validity of the theoretical results.