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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 429076, 12 pages
Dynamic Behaviors of a Discrete Two Species Predator-Prey System Incorporating Harvesting
Department of Mathematics, Minjiang University, Fujian, Fuzhou 350108, China
Received 2 May 2012; Revised 19 August 2012; Accepted 29 August 2012
Academic Editor: Jinde Cao
Copyright © 2012 Ting Wu. 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.
- F. D. Chen, “Persistence and global stability for nonautonomous cooperative system with diffusion and time delay,” Acta Scientiarum Naturalium Universitatis Pekinensis, vol. 39, no. 1, pp. 22–28, 2003.
- T. Wu, “Permanence for nonautonomous Lotka-Volterra tow species cooperatative systems,” Bulletin of Science and Technology, vol. 25, no. 6, pp. 743–746, 2009 (Chinese).
- T. Wu, “Permanence and global stability of a discrete competition feedback-control system with Beddington-DeAngelis functional response,” Journal of Minjiang University (Natural Science Edition), vol. 31, no. 2, pp. 16–20, 2010 (Chinese).
- T. Wu, “Permanence of discrete predator-prey system with infinite delay Beddington-DeAngelis functional response,” Journal of Minjiang University (Natural Science Edition), vol. 31, no. 5, pp. 1–5, 2010 (Chinese).
- C. W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources, John Wiley & Sons, New York, NY, USA, 2nd edition, 1990.
- P. H. Leslie, “Some further notes on the use of matrices in population mathematics,” Biometrika, vol. 35, pp. 213–245, 1948.
- P. H. Leslie, “A stochastic model for studying the properties of certain biological systems by numerical methods,” Biometrika, vol. 45, pp. 16–31, 1958.
- A. Korobeinikov, “A Lyapunov function for Leslie-Gower predator-prey models,” Applied Mathematics Letters, vol. 14, no. 6, pp. 697–699, 2001.
- N. Zhang, F. D. Chen, Q. Q. Su, and T. Wu, “Dynamic behaviors of a harvesting Leslie-Gower predator-prey model,” Discrete Dynamics in Nature and Society, vol. 655, no. 10, pp. 1–10, 2011.
- D. Hu and Z. Zhang, “Four positive periodic solutions of a discrete time delayed predator-prey system with nonmonotonic functional response and harvesting,” Computers & Mathematics with Applications, vol. 56, no. 12, pp. 3015–3022, 2008.
- 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. 373–389, 1996.
- K. S. Chaudhuri, “A bioeconomic model of harvesting amultispecies fishery,” Ecological Modelling, vol. 32, no. 4, pp. 267–279, 1986.
- K. S. Chaudhuri, “Dynamic optimization of combined harvesting of a two-species fishery,” Ecological Modelling, vol. 41, no. 1-2, pp. 17–25, 1988.
- T. K. Kar, “Modelling and analysis of a harvested prey-predator system incorporating a prey refuge,” Journal of Computational and Applied Mathematics, vol. 185, no. 1, pp. 19–33, 2006.
- M. Fan and K. Wang, “Optimal harvesting policy for single population with periodic coefficients,” Mathematical Biosciences, vol. 152, no. 2, pp. 165–177, 1998.
- C. W. Clark, Bioeconomic Modeling and Fisheries Management, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1985.
- L. Wang and M. Q. Wang, Ordinary Difference Equation, Xinjiang University Press, Xinjiang, China, 1991.