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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.

Linked References

  1. H. Zhang, X.-Z. Meng, and L.-S. Chen, “Impact of impulsive effect on a population dynamical behavior in a polluted environment,” Journal of Dalian University of Technology, vol. 48, no. 1, pp. 147–153, 2008. View at Google Scholar · View at Scopus
  2. X. F. Yan, H. Yin, Y. Cao et al., “The survival analysis of single population in a polluted environment,” Journal of Biomathematics, vol. 24, no. 1, pp. 87–92, 2009. View at Google Scholar
  3. X. Liu and M. Li, “Mathematical study on a single species model with pollution abatement,” Journal of Biomathematics, vol. 28, no. 1, pp. 118–122, 2013. View at Google Scholar · View at MathSciNet
  4. Q. Zhang, C. Liu, and X. Zhang, Complexity, Analysis and Control of Singular Biological Systems, vol. 421 of Lecture Notes in Control and Information Sciences, Springer, 2012.
  5. B. Chen and J. Chen, “Bifurcation and chaotic behavior of a discrete singular biological economic system,” Applied Mathematics and Computation, vol. 219, no. 5, pp. 2371–2386, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. Y. Zhang, Q. L. Zhang, and L. C. Zhao, “Tracking control of class in singular biological economy systems,” Journal of Northeastern University (Natural Science), vol. 28, no. 2, pp. 157–160, 2007. View at Google Scholar
  7. J.-H. Li, L. Cui, Y.-H. Yu, and L.-G. Zhang, “Limit cycle and chaos of an epidemic model with varying total population size,” Mathematics in Practice and Theory, vol. 38, no. 10, pp. 133–135, 2008. View at Google Scholar
  8. W. Liu, C. J. Fu, and B. S. Chen, “Hopf bifurcation and center stability for a predator-prey biological economic model with prey harvesting,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 10, pp. 3989–3998, 2012. View at Publisher · View at Google Scholar · View at Scopus
  9. F. Zhao, Q. L. Zhang, and Y. Zhang, “H-infinity filtering for a class of singular biological systems,” IET Control Theory and Applications, vol. 9, no. 13, pp. 2044–2055, 2015. View at Google Scholar
  10. D. X. Zou and C. Liu, “Bifurcation and control for singular prey-predator system with stage structure,” Journal of Biomathematics, vol. 24, no. 4, pp. 711–720, 2009. View at Google Scholar
  11. L. Li, Q. Zhang, and B. Zhu, “Fuzzy stochastic optimal guaranteed cost control of bio-economic singular Markovian jump systems,” IEEE Transactions on Cybernetics, vol. 45, no. 11, pp. 2512–2521, 2015. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Aditya and D. Prodromos, Control of Nonlinear Differential Algebraic Equation Systems with Applications to Chemical Processes, Hapman & Hall/CRC, London, UK, 1999.
  13. W. Marszalek and Z. W. Trzaska, “Singularity-induced bifurcations in electrical power systems,” IEEE Transactions on Power Systems, vol. 20, no. 1, pp. 312–320, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. Q.-H. Wang and S.-X. Zhou, “Singularity induced bifurcation in power system differential algebraic model,” Proceedings of the Chinese Society of Electrical Engineering, vol. 23, no. 7, pp. 18–22, 2003. View at Google Scholar · View at Scopus
  15. M. Yue and R. Schlueter, “Bifurcation subsystem and its application in power system analysis,” IEEE Transactions on Power Systems, vol. 19, no. 4, pp. 1885–1893, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. Q. L. Zhang, H. Niu, L. C. Zhao, and F. Bai, “The analysis and control for singular ecological-economic model with harvesting and migration,” Journal of Applied Mathematics, vol. 2012, Article ID 973869, 17 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. N. Li, H.-Y. Sun, and Q.-L. Zhang, “The dynamics and bifurcation control of a singular biological economic model,” International Journal of Automation and Computing, vol. 9, no. 1, pp. 1–7, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. Zhang, Q. L. Zhang, and L. C. Zhao, “Analysis and feedback control for a class of bioeconomic systems,” Control Engineering of China, vol. 14, no. 6, pp. 599–603, 2007. View at Google Scholar
  19. Y. Zhang, Q. L. Zhang, and L. C. Zhao, “Bifurcations and control in singular biological economic model with stage structure,” Journal of System Engineering, vol. 22, no. 3, pp. 233–238, 2007. View at Google Scholar
  20. S. Luan, B. Liu, and L. X. Zhang, “Dynamics on a single-species model in a polluted environment,” Journal of Biomathematics, vol. 26, no. 4, pp. 689–694, 2011. View at Google Scholar
  21. H. S. Gordon, “The economic theory of a common-property resource: the fishery,” Journal of Political Economy, vol. 62, no. 2, pp. 124–142, 1954. View at Publisher · View at Google Scholar
  22. V. Norris, M. Engel, and M. Demarty, “Modelling biological systems with competitive coherence,” Advances in Artificial Neural Systems, vol. 2012, Article ID 703878, 20 pages, 2012. View at Publisher · View at Google Scholar
  23. A. J. Lotka, Elements of Mathematical Biology, Cambrige University Press, Cambridge, UK, 2001.
  24. F. Yu, Q. Meng, and X. N. Fan, “A discussion on application for Routh-Hurwitz criterion,” Journal of Electrical and Electronic Education, vol. 35, no. 1, pp. 12–14, 2013. View at Google Scholar
  25. V. Venkatasubramanian, H. Schattler, and J. Zaborszky, “Local bifurcations and feasibility regions in differential-algebraic systems,” IEEE Transactions on Automatic Control, vol. 40, no. 12, pp. 1992–2013, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  26. China environment protection database, http://hbk.cei.gov.cn/aspx/default.aspx.
  27. H. Yu, Study on the Method of Assessment for Environment Pollution Accidents, Science Press, Beijing, China, 2012.