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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 508962, 14 pages
Dynamic Behaviors of a Nonautonomous Discrete Predator-Prey System Incorporating a Prey Refuge and Holling Type II Functional Response
College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China
Received 1 October 2012; Revised 11 December 2012; Accepted 12 December 2012
Academic Editor: M. De la Sen
Copyright © 2012 Yumin Wu 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.
- A. A. Berryman, “The origins and evolution of predator-prey theory,” Ecology, vol. 75, no. 5, pp. 1530–1535, 1992.
- Y. Wang and J. Wang, “Influence of prey refuge on predator-prey dynamics,” Nonlinear Dynamics, vol. 67, no. 1, pp. 191–201, 2012.
- H. I. Freedman, Deterministic Mathematical Models in Population Ecology, vol. 57, Marcel Dekker, New York, NY, USA, 1980.
- A. Sih, “Prey refuges and predator-prey stability,” Theoretical Population Biology, vol. 31, no. 1, pp. 1–12, 1987.
- E. González-Olivares and R. Ramos-Jiliberto, “Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability,” Ecological Modelling, vol. 166, no. 1-2, pp. 135–146, 2003.
- T. K. Kar, “Stability analysis of a prey-predator model incorporating a prey refuge,” Communications in Nonlinear Science and Numerical Simulation, vol. 10, no. 6, pp. 681–691, 2005.
- 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.
- Z. S. Shuai, C. M. Miao, W. P. Zhang, D. Ye, and K. Wang, “A three-species prey-predator model with refuges,” Journal of Biomathematics, vol. 19, no. 1, pp. 65–71, 2004 (Chinese).
- J. Zhu and H. M. Liu, “Permanence of the two interacting prey-predator with refuges,” Journal of Northwest University For Nationalities, vol. 27, no. 62, pp. 1–3, 2006 (Chinese).
- G. M. Xu and X. H. Chen, “Persistence and periodic solution for three interacting predator-prey system with refuges,” Yinshan Academic Journal, vol. 23, no. 1, pp. 14–17, 2009 (Chinese).
- G. M. Xu and J. W. Jia, “Stability analysis of a predator-prey system with refuges,” Journal of Shanxi Normal University, vol. 21, no. 4, pp. 4–7, 2007 (Chinese).
- J. D. Murry, Mathematical Biology, Springer, New York, NY, USA, 1989.
- F. Chen, “Permanence for the discrete mutualism model with time delays,” Mathematical and Computer Modelling, vol. 47, no. 3-4, pp. 431–435, 2008.
- S. P. Yu, W. T. Xiong, and H. Qi, “A ratio-dependent one-predator two-competing-prey model with delays and refuges,” Mathematica Applicata, vol. 23, no. 1, pp. 198–203, 2010.
- Y. B. Zhang, W. X. Wang, and Y. H. Duan, “Analysis of prey-predator with Holling III functional response and prey refuge,” Mathematics in Practice and Theory, vol. 40, no. 24, pp. 149–154, 2010 (Chinese).
- Z. Li and F. Chen, “Extinction in two dimensional discrete Lotka-Volterra competitive system with the effect of toxic substances,” Dynamics of Continuous, Discrete and Impulsive Systems B, vol. 15, no. 2, pp. 165–178, 2008.
- K. Zhuang and Z. Wen, “Dynamical behaviors in a discrete predator-prey model with a prey refuge,” International Journal of Computational and Mathematical Sciences, vol. 5, no. 4, pp. 195–197, 2011.
- Y. Chen and Z. Zhou, “Stable periodic solution of a discrete periodic Lotka-Volterra competition system,” Journal of Mathematical Analysis and Applications, vol. 277, no. 1, pp. 358–366, 2003.
- C. Ji, D. Jiang, and X. Li, “Qualitative analysis of a stochastic ratio-dependent predator-prey system,” Journal of Computational and Applied Mathematics, vol. 235, no. 5, pp. 1326–1341, 2011.
- A. Yagi and T. V. Ton, “Dynamic of a stochastic predator-prey population,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3100–3109, 2011.
- J. Lv and K. Wang, “Asymptotic properties of a stochastic predator-prey system with Holling II functional response,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 10, pp. 4037–4048, 2011.