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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 713503, 14 pages
Multiple Periodic Solutions of a Ratio-Dependent Predator-Prey Discrete Model
College of Science, Hunan Agricultural University, Changsha, Hunan 410128, China
Received 29 September 2012; Accepted 6 December 2012
Academic Editor: Xiang Ping Yan
Copyright © 2012 Tiejun Zhou 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.
- C. S. Holling, “The functional response of predator to prey density and its role in mimicry and population regulation,” Memoirs of the Entomological Society of Canada, vol. 97, no. 45, pp. 1–60, 1965.
- J. F. Andrews, “A mathematical model for the continuous culture of microorganisms utilizing inhabitory substrates,” Biotechnology and Bioengineering, no. 10, pp. 707–723, 1968.
- H. Y. Lu and W. G. Wang, “Dynamics of a delayed discrete semi-ratio-dependent predator-prey system with Holling type IV functional response,” Advances in Difference Equations, vol. 2011, no. 1, pp. 1–19, 2011.
- W. Yang and X. Li, “Permanence for a delayed discrete ratio-dependent predator-prey model with monotonic functional responses,” Nonlinear Analysis. Real World Applications, vol. 10, no. 2, pp. 1068–1072, 2009.
- S. Ruan and D. Xiao, “Global analysis in a predator-prey system with nonmonotonic functional response,” SIAM Journal on Applied Mathematics, vol. 61, no. 4, pp. 1445–1472, 2001.
- Y. Xia, J. Cao, and S. S. Cheng, “Multiple periodic solutions of a delayed stage-structured predator-prey model with non-monotone functional responses,” Applied Mathematical Modelling, vol. 31, no. 9, pp. 1947–1959, 2007.
- 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.
- Z. Hu, Z. Teng, and L. Zhang, “Stability and bifurcation analysis of a discrete predator-prey model with nonmonotonic functional response,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 2356–2377, 2011.
- Y. Xia, J. Cao, and M. Lin, “Discrete-time analogues of predator-prey models with monotonic or nonmonotonic functional responses,” Nonlinear Analysis: Real World Applications, vol. 8, no. 4, pp. 1079–1095, 2007.
- Y.-H. Fan and L.-L. Wang, “Periodic solutions in a delayed predator-prey model with nonmonotonic functional response,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 3275–3284, 2009.
- X. Ding, C. Lu, and M. Liu, “Periodic solutions for a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay,” Nonlinear Analysis: Real World Applications, vol. 9, no. 3, pp. 762–775, 2008.
- R. Arditi and L. R. Ginzburg, “Coupling in predator-prey dynamics: ratio-dependence,” Journal of Theoretical Biology, vol. 139, pp. 311–326, 1989.
- M. Fan, Q. Wang, and X. Zou, “Dynamics of a non-autonomous ratio-dependent predator-prey system,” Proceedings of the Royal Society of Edinburgh, vol. 133, no. 1, pp. 97–118, 2003.
- M. Fan and K. Wang, “Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system,” Mathematical and Computer Modelling, vol. 35, no. 9-10, pp. 951–961, 2002.
- Y. Xia and M. Han, “Multiple periodic solutions of a ratio-dependent predator-prey model,” Chaos, Solitons & Fractals, vol. 39, no. 3, pp. 1100–1108, 2009.
- G. Chen, Z. Teng, and Z. Hu, “Analysis of stability for a discrete ratio-dependent predator-prey system,” Indian Journal of Pure and Applied Mathematics, vol. 42, no. 1, pp. 1–26, 2011.
- Y.-H. Fan and L.-L. Wang, “On a generalized discrete ratio-dependent predator-prey system,” Discrete Dynamics in Nature and Society, Article ID 653289, 22 pages, 2009.
- C. Lu and L. Zhang, “Permanence and global attractivity of a discrete semi-ratio dependent predator-prey system with Holling II type functional response,” Journal of Applied Mathematics and Computing, vol. 33, no. 1-2, pp. 125–135, 2010.
- J. H. Yang, “Dynamics behaviors of a discrete ratio-dependent predator-prey system with holling type III functional response and feedback controls,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 186539, 19 pages, 2008.
- R. E. Gaines and J. L. Mawhin, Coincidence Degree, and Nonlinear Differential Equations, Springer, Berlin, Germany, 1977.