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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 5036305, 10 pages
Research Article

The Modeling and Control of a Singular Biological Economic System with Time Delay in a Polluted Environment

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

Received 16 July 2016; Accepted 20 September 2016

Academic Editor: Daniele Fournier-Prunaret

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.


This paper brings up the idea of a biological economic system with time delay in a polluted environment. Firstly, by proper linear transformation and parametric method, the singular time-delay systems are transformed to differential time-delay systems. Then, using center manifold theory and Poincare normal form method, the direction of Hopf bifurcation and the stability and period of its periodic orbits are analysed. At last, we have performed numerical simulation to support the analytical results.