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Mathematical Problems in Engineering
Volume 2012, Article ID 803270, 17 pages
http://dx.doi.org/10.1155/2012/803270
Research Article

Dynamics and Optimal Taxation Control in a Bioeconomic Model with Stage Structure and Gestation Delay

1State Key Laboratory of Integrated Automation of Process Industry, Institute of Systems Science, Northeastern University, Shenyang 110004, China
2School of Science, Shenyang University of Technology, Shenyang 110870, China
3School of Science, Dalian Jiaotong University, Dalian 116028, China

Received 17 February 2012; Accepted 1 May 2012

Academic Editor: Moez Feki

Copyright © 2012 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. K. Yang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, Calif, USA, 1993. View at Zentralblatt MATH
  2. O. Arino, E. Sánchez, and A. Fathallah, “State-dependent delay differential equations in population dynamics: modeling and analysis,” in Fields Institute Communications, vol. 29, pp. 19–36, American Mathematical Society, Providence, RI, USA, 2001. View at Google Scholar · View at Zentralblatt MATH
  3. X. Song and L. Chen, “Optimal harvesting and stability for a two-species competitive system with stage structure,” Mathematical Biosciences, vol. 170, no. 2, pp. 173–186, 2001. View at Publisher · View at Google Scholar
  4. J. Al-Omari and S. A. Gourley, “Monotone travelling fronts in an age-structured reaction-diffusion model of a single species,” Journal of Mathematical Biology, vol. 45, no. 4, pp. 294–312, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. T. K. Kar, “Selective harvesting in a prey-predator fishery with time delay,” Mathematical and Computer Modelling, vol. 38, no. 3-4, pp. 449–458, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. R. Xu, M. A. J. Chaplain, and F. A. Davidson, “Persistence and stability of a stage-structured predator-prey model with time delays,” Applied Mathematics and Computation, vol. 150, no. 1, pp. 259–277, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. S. A. Gourley and Y. Kuang, “A stage structured predator-prey model and its dependence on maturation delay and death rate,” Journal of Mathematical Biology, vol. 49, no. 2, pp. 188–200, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. M. Bandyopadhyay and S. Banerjee, “A stage-structured prey-predator model with discrete time delay,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1385–1398, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. R. Xu and Z. Ma, “Stability and Hopf bifurcation in a predator-prey model with stage structure for the predator,” Nonlinear Analysis. Real World Applications, vol. 9, no. 4, pp. 1444–1460, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. C. W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resource, John Wiley & Sons, New York, NY, USA, 2nd edition, 1990.
  11. S. Ganguly and K. S. Chaudhuri, “Regulation of a single-species fishery by taxation,” Ecological Modelling, vol. 82, no. 1, pp. 51–60, 1995. View at Publisher · View at Google Scholar
  12. S. V. Krishna, P. D. N. Srinivasu, and B. Kaymakcalan, “Conservation of an ecosystem through optimal taxation,” Bulletin of Mathematical Biology, vol. 60, no. 3, pp. 569–584, 1998. View at Publisher · View at Google Scholar
  13. B. Dubey, P. Chandra, and P. Sinha, “A resource dependent fishery model with optimal harvesting policy,” Journal of Biological Systems, vol. 10, no. 1, pp. 1–13, 2002. View at Publisher · View at Google Scholar
  14. B. Dubey, P. Sinha, and P. Chandra, “A model for an inshore-offshore fishery,” Journal of Biological Systems, vol. 11, no. 1, pp. 27–41, 2003. View at Publisher · View at Google Scholar
  15. K. Chaudhuri, “A bioeconomic model of harvesting a multispecies fishery,” Ecological Modelling, vol. 32, no. 4, pp. 267–279, 1986. View at Google Scholar
  16. K. Chaudhuri, “Dynamic optimization of combined harvesting of a two-species fishery,” Ecological Modelling, vol. 41, no. 1-2, pp. 17–25, 1988. View at Google Scholar
  17. S. S. Sana, D. Purohit, and K. Chaudhuri, “Joint project of fishery and poultry-a bioeconomic model,” Applied Mathematical Modelling, vol. 36, no. 1, pp. 72–86, 2012. View at Publisher · View at Google Scholar
  18. T. Pradhan and K. S. Chaudhuri, “A dynamic reaction model of a two-species fishery with taxation as a control instrument: a capital theoretic analysis,” Ecological Modelling, vol. 121, no. 1, pp. 1–16, 1999. View at Publisher · View at Google Scholar
  19. T. K. Kar and K. S. Chaudhuri, “Regulation of a prey-predator fishery by taxation: a dynamic reaction model,” Journal of Biological Systems, vol. 11, no. 2, pp. 173–187, 2003. View at Publisher · View at Google Scholar
  20. T. K. Kar, U. K. Pahari, and K. S. Chaudhuri, “Management of a prey-predator fishery based on continuous fishing effort,” Journal of Biological Systems, vol. 12, no. 3, pp. 301–313, 2004. View at Publisher · View at Google Scholar
  21. T. K. Kar, “Management of a fishery based on continuous fishing effort,” Nonlinear Analysis. Real World Applications, vol. 5, no. 4, pp. 629–644, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. T. K. Kar, “Conservation of a fishery through optimal taxation: a dynamic reaction model,” Communications in Nonlinear Science and Numerical Simulation, vol. 10, no. 2, pp. 121–131, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. T. K. Kar and K. Chakraborty, “Effort dynamic in a prey-predator model with harvesting,” International Journal of Information & Systems Sciences, vol. 6, no. 3, pp. 318–332, 2010. View at Google Scholar
  24. K. Chakraborty, M. Chakraborty, and T. K. Kar, “Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay,” Nonlinear Analysis. Hybrid Systems, vol. 5, no. 4, pp. 613–625, 2011. View at Publisher · View at Google Scholar
  25. S. S. Sana, “An integrated project of fishery and poultry,” Mathematical and Computer Modelling, vol. 54, no. 1-2, pp. 35–49, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. C. Liu, Q. Zhang, J. Huang, and W. Tang, “Dynamical behavior of a harvested prey-predator model with stage structure and discrete time delay,” Journal of Biological Systems, vol. 17, no. 4, pp. 759–777, 2009. View at Publisher · View at Google Scholar
  27. X. Yang, L. Chen, and J. Chen, “Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models,” Computers and Mathematics with Applications, vol. 32, no. 4, pp. 109–116, 1996. View at Publisher · View at Google Scholar
  28. H. R. Thieme, Mathematics in Population Biology, Princeton University Press, Princeton, NJ, USA, 2003.
  29. J. K. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 1997.
  30. M. Kot, Elements of Mathematical Ecology, Cambridge University Press, Cambridge, UK, 2001. View at Publisher · View at Google Scholar
  31. D. N. Burghes and A. Graham, Introduction to Control Theory, Including Optimal Control, John Wiley & Sons, New York, NY, USA, 1980.
  32. K. J. Arrow and M. Kurz, Public Investment, The rate of Return and Optimal Fiscal Policy, John Hopkins, Baltimore, Md, USA, 1970.