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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 605471, 8 pages
Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System
College of Mathematics and Information Science, Henan Normal University, 453007, China
Received 20 July 2013; Revised 4 September 2013; Accepted 4 September 2013
Academic Editor: Yanni Xiao
Copyright © 2013 Xia Liu and Jinling Wang. 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.
- D. M. Xiao and S. G. Ruan, “Codimension two bifurcations in a predator-prey system with group defense,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 11, no. 8, pp. 2123–2131, 2001.
- D. Xiao, W. Li, and M. Han, “Dynamics in a ratio-dependent predator-prey model with predator harvesting,” Journal of Mathematical Analysis and Applications, vol. 324, no. 1, pp. 14–29, 2006.
- L. L. Wang, Y. H. Fan, and W. T. Li, “Multiple bifurcations in a predator-prey system with monotonic functional response,” Applied Mathematics and Computation, vol. 172, no. 2, pp. 1103–1120, 2006.
- Y. L. Li and D. M. Xiao, “Bifurcations of a predator-prey system of Holling and Leslie types,” Chaos, Solitons & Fractals, vol. 34, no. 2, pp. 606–620, 2007.
- T. Faria and L. T. Magalhaes, “Normal forms for retarded functional-differential equations and applications to Bogdanov-Takens singularity,” Journal of Differential Equations, vol. 122, no. 2, pp. 201–224, 1995.
- D. M. Xiao and S. G. Ruan, “Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response,” Journal of Differential Equations, vol. 176, no. 2, pp. 494–510, 2001.
- J. Xia, Z. Liu, R. Yuan, and S. Ruan, “The effects of harvesting and time delay on predator-prey systems with Holling type II functional response,” SIAM Journal on Applied Mathematics, vol. 70, no. 4, pp. 1178–1200, 2009.
- S. A. Campbell and Y. Yuan, “Zero singularities of codimension two and three in delay differential equations,” Nonlinearity, vol. 21, no. 11, pp. 2671–2691, 2008.
- Z. Q. Qiao, X. B. Liu, and D. M. Zhu, “Bifurcation in delay differential systems with triple-zero singularity,” Chinese Annals of Mathematics A, vol. 31, no. 1, pp. 59–70, 2010.
- X. He, C. D. Li, and Y. L. Shu, “Triple-zero bifurcation in van der Pol's oscillator with delayed feedback,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 12, pp. 5229–5239, 2012.
- R. P. Gupta and P. Chandra, “Bifurcation analysis of modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting,” Journal of Mathematical Analysis and Applications, vol. 398, no. 1, pp. 278–295, 2013.
- A. F. Nindjin, M. A. Aziz-Alaoui, and M. Cadivel, “Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay,” Nonlinear Analysis: Real World Applications, vol. 7, no. 5, pp. 1104–1118, 2006.
- R. Yafia, F. E. Adnani, and H. T. Alaoui, “Limit cycle and numerical similations for small and large delays in a predator-prey model with modified Leslie-Gower and Holling-type II schemes,” Nonlinear Analysis: Real World Applications, vol. 9, no. 5, pp. 2055–2067, 2008.
- Y. X. Xu and M. Y. Huang, “Homoclinic orbits and Hopf bifurcations in delay differential systems with T-B singularity,” Journal of Differential Equations, vol. 244, no. 3, pp. 582–598, 2008.
- Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, vol. 112 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1995.
- F. Y. Lian and Y. T. Xu, “Hopf bifurcation analysis of a predator-prey system with Holling type IV functional response and time delay,” Applied Mathematics and Computation, vol. 215, no. 4, pp. 1484–1495, 2009.
- J. K. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 1997.