Table of Contents Author Guidelines Submit a Manuscript
Journal of Mathematics
Volume 2013, Article ID 613706, 9 pages
http://dx.doi.org/10.1155/2013/613706
Research Article

A Mathematical Model for Optimal Management and Utilization of a Renewable Resource by Population

Department of Mathematics, Birla Institute of Technology & Science, Pilani 333031, India

Received 20 August 2012; Accepted 20 October 2012

Academic Editor: Kaleem R. Kazmi

Copyright © 2013 B. Dubey and Atasi Patra. 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. C. W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resource, John Wiley & Sons, New York, NY, USA, 1976. View at Zentralblatt MATH · View at MathSciNet
  2. C. W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resource, John Wiley & Sons, New York, NY, USA, 2nd edition, 1990. View at Zentralblatt MATH · View at MathSciNet
  3. D. K. Bhattacharya and S. Begum, “Bionomic equilibrium of two-species system,” Mathematical Biosciences, vol. 135, no. 2, pp. 111–127, 1996. View at Publisher · View at Google Scholar · View at Scopus
  4. K. S. Chaudhuri and T. Johnson, “Bioeconomic dynamics of a fishery modeled as an S-system,” Mathematical Biosciences, vol. 99, no. 2, pp. 231–249, 1990. View at Publisher · View at Google Scholar · View at Scopus
  5. K. S. Chaudhuri and S. Saha Roy, “Bioeconomic exploitation of a lotka-volterra prey-predator system,” Bulletin of Calcutta Mathematical Society, vol. 83, pp. 175–186, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. K. S. Chaudhuri and S. S. Ray, “On the combined harvesting of a prey-predator system,” Journal of Biological Systems, vol. 4, no. 3, pp. 376–389, 1996. View at Google Scholar · View at Scopus
  7. T. K. Kar and K. S. Chaudhuri, “Harvesting in a two-prey one-predator fishery: a bioeconomic model,” ANZIAM Journal, vol. 45, no. 3, pp. 443–456, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. T. K. Kar, S. Misra, and B. Mukhopadhyay, “A bioeconomic model of a ratio-dependent predator-prey system and optimal harvesting,” Journal of Applied Mathematics and Computing, vol. 22, no. 1-2, pp. 387–401, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. T. K. Kar and H. Matsuda, “Controllability of a harvested prey-predator system with time delay,” Journal of Biological Systems, vol. 14, no. 2, pp. 1–12, 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. 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 · View at Scopus
  11. B. Dubey, P. Chandra, and P. Sinha, “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 · View at Scopus
  12. B. Dubey, P. Chandra, and P. Sinha, “A model for fishery resource with reserve area,” Nonlinear Analysis: Real World Applications, vol. 4, no. 4, pp. 625–637, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. A. Leung and A. Y. Wang, “Analysis of models for commercial fishing : mathematical and economic aspects,” Econometrica, vol. 44, pp. 295–303, 1976. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. K. S. Chaudhuri, “A bioeconomic model of harvesting a multispecies fishery,” Ecological Modelling, vol. 32, no. 4, pp. 267–279, 1986. View at Google Scholar · View at Scopus
  15. D. L. Ragozin and G. Brown Jr., “Harvest policies and non-market valuation in a predator-prey system,” Journal of Environmental Economics and Management, vol. 12, pp. 155–168, 1985. View at Google Scholar
  16. M. Mesterton-Gibbons, “On the optimal policy for combined harvesting of predator-prey,” Natural Resource Modeling, vol. 3, pp. 63–90, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. Mesterton-Gibbons, “A technique for finding optimal two-species harvesting policies,” Ecological Modelling, vol. 92, no. 2-3, pp. 235–244, 1996. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Fan and K. Wang, “Optimal harvesting policy for single population with periodic coefficients,” Mathematical Biosciences, vol. 152, no. 2, pp. 165–177, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. X. Zhang, L. Chen, and A. U. Neumann, “The stage-structured predator-prey model and optimal harvesting policy,” Mathematical Biosciences, vol. 168, no. 2, pp. 201–210, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. 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 · View at MathSciNet · View at Scopus
  21. T. K. Kar, S. K. Chottopadhayay, and C. K. Pati, “A bio-economic model of two-prey one predator system,” Journal of Applied Mathematics and Informatics, vol. 27, no. 5-6, pp. 1411–1427, 2009. View at Google Scholar
  22. T. K. Kar and S. K. Chottopadhayay, “Bioeconomic moddelling: an application to the north-east atlantic cod fishery,” Journal of Mathematics Research, vol. 1, no. 2, pp. 164–178, 2009. View at Google Scholar
  23. T. K. Kar, S. K. Chattopadhyay, and R. P. Agarwal, “Dynamics of an exploited prey-predator system with non-monotonic functional response,” Communications in Applied Analysis, vol. 14, no. 1, pp. 21–38, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  24. H. I. Freedman and J. W. H. So, “Global stability and persistence of simple food chain,” Mathematical Biosciences, vol. 76, no. 1, pp. 69–86, 1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  25. J. B. Shukla and B. Dubey, “Modelling the depletion and conservation of forestry resources: effects of population and pollution,” Journal of Mathematical Biology, vol. 36, no. 1, pp. 71–94, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. Y. Louartassi, N. Elalami, and E. H. El Mazoudi, “Stability analysis and static output feedback design for a model the fishery resource with reserve area,” Applied Mathematical Sciences, vol. 6, no. 66, pp. 3289–3299, 2012. View at Google Scholar
  27. E. El Mazoudi, N. Elalami, and M. Mrabti, “Output feedback control for an exploited structured model of a fishing problem,” Journal of Biological Systems, vol. 16, no. 1, pp. 107–117, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus