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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 628103, 19 pages
A Predator-Prey Model with Functional Response and Stage Structure for Prey
1School of Mathematics and Statistics, Tianshui Normal University, Tianshui, Gansu 741001, China
2Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
Received 24 September 2011; Accepted 25 November 2011
Academic Editor: Muhammad Aslam Noor
Copyright © 2012 Xiao-Ke Sun 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.
- E. Beretta and Y. Kuang, “Geometric stability switch criteria in delay differential systems with delay dependent parameters,” SIAM Journal on Mathematical Analysis, vol. 33, no. 5, pp. 1144–1165, 2002.
- Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1993.
- X.-Y. Song and L.-S. Chen, “Optimal harvesting and stability for a predator-prey system with stage structure,” Acta Mathematicae Applicatae Sinica, vol. 18, no. 3, pp. 423–430, 2002.
- W. Wang and L. Chen, “A predator-prey system with stage-structure for predator,” Computers & Mathematics with Applications, vol. 33, no. 8, pp. 83–91, 1997.
- S. A. Gourley and Y. Kuang, “A stage structured predator-prey model and its dependence on maturation delay and death rate,” Journal of Mathematical Biology, vol. 49, no. 2, pp. 188–200, 2004.
- S. Liu and J. Zhang, “Coexistence and stability of predator-prey model with Beddington-DeAngelis functional response and stage structure,” Journal of Mathematical Analysis and Applications, vol. 342, no. 1, pp. 446–460, 2008.
- L. Ou, G. Luo, Y. Jiang, and Y. Li, “The asymptotic behaviors of a stage-structured autonomous predator-prey system with time delay,” Journal of Mathematical Analysis and Applications, vol. 283, no. 2, pp. 534–548, 2003.
- W. G. Aiello, H. I. Freedman, and J. Wu, “Analysis of a model representing stage-structured population growth with state-dependent time delay,” SIAM Journal on Applied Mathematics, vol. 52, no. 3, pp. 855–869, 1992.
- F. Y. Wang and G. P. Pang, “The global stability of a delayed predator-prey system with two stage-structure,” Chaos, Solitons & Fractals, vol. 10, pp. 1016–1023, 2007.
- S. Gao, L. Chen, and L. Sun, “Optimal pulse fishing policy in stage-structured models with birth pulses,” Chaos, Solitons & Fractals, vol. 25, no. 5, pp. 1209–1219, 2005.
- X. Y. Li and W. Wang, “A discrete epidemic model with stage structure,” Chaos, Solitons & Fractals, vol. 26, no. 3, pp. 947–958, 2005.
- X. K. Sun and H. F. Huo, “Permanence of a Holling type II predator-prey system with stagestructure,” in Proceedings of the 6th Conference of Biomathematics, vol. 2, pp. 598–602, Advanced Biomedical, Tai’an, China, July 2008.
- W. Wang, P. Fergola, S. Lombardo, and G. Mulone, “Mathematical models of innovation diffusion with stage structure,” Applied Mathematical Modelling, vol. 30, no. 1, pp. 129–146, 2006.
- S. Y. Tang and L. S. Chen, “Multiple attractors in stage-structured population models with birth pulses,” Bulletin of Math Biology, vol. 65, pp. 479–495, 2003.
- Y. Xiao, D. Cheng, and S. Tang, “Dynamic complexities in predator-prey ecosystem models with age-structure for predator,” Chaos, Solitons & Fractals, vol. 14, no. 9, pp. 1403–1411, 2002.
- X. Song, L. Cai, and A. U. Neumann, “Ratio-dependent predator-prey system with stage structure for prey,” Discrete and Continuous Dynamical Systems B, vol. 4, no. 3, pp. 747–758, 2004.
- F. Chen, “Permanence of periodic Holling type predator-prey system with stage structure for prey,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1849–1860, 2006.
- F. Chen and M. You, “Permanence, extinction and periodic solution of the predator-prey system with Beddington-DeAngelis functional response and stage structure for prey,” Nonlinear Analysis: Real World Applications, vol. 9, no. 2, pp. 207–221, 2008.
- J. Cui and Y. Takeuchi, “A predator-prey system with a stage structure for the prey,” Mathematical and Computer Modelling, vol. 44, no. 11-12, pp. 1126–1132, 2006.
- C.-Y. Huang, M. Zhao, and L.-C. Zhao, “Permanence of periodic predator-prey system with two predators and stage structure for prey,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 503–514, 2010.
- H. Zhang, L. Chen, and R. Zhu, “Permanence and extinction of a periodic predator-prey delay system with functional response and stage structure for prey,” Applied Mathematics and Computation, vol. 184, no. 2, pp. 931–944, 2007.
- X.-K. Sun, H.-F. Huo, and H. Xiang, “Bifurcation and stability analysis in predator-prey model with a stage-structure for predator,” Nonlinear Dynamics, vol. 58, no. 3, pp. 497–513, 2009.