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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 795358, 12 pages
Stability and Hopf Bifurcation Analysis for a Gause-Type Predator-Prey System with Multiple Delays
1Department of Science, Bengbu College, Bengbu 233030, China
2Department of Mechanical and Electronic Engineering, Bengbu College, Bengbu 233030, China
3Faculty of Science, Jiangsu University, Zhenjiang 212013, China
Received 5 May 2013; Accepted 13 May 2013
Academic Editor: Luca Guerrini
Copyright © 2013 Juan Liu 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. Klebanoff and A. Hastings, “Chaos in three-species food chains,” Journal of Mathematical Biology, vol. 32, no. 5, pp. 427–451, 1994.
- M. C. Varriale and A. A. Gomes, “A study of a three species food chain,” Ecological Modelling, vol. 110, no. 2, pp. 119–133, 1998.
- H. I. Freedman and P. Waltman, “Mathematical analysis of some three-species food-chain models,” Mathematical Biosciences, vol. 33, no. 3-4, pp. 257–276, 1977.
- K. McCann and P. Yodzis, “Bifurcation structure of a 3-species food chain model,” Theoretical Population Biology, vol. 48, no. 2, pp. 93–125, 1995.
- A. Hastings and T. Powell, “Chaos in three-species food chain,” Ecology, vol. 72, no. 3, pp. 896–903, 1991.
- S. Guo and W. Jiang, “Global stability and Hopf bifurcation for Gause-type predator-prey system,” Journal of Applied Mathematics, vol. 2012, Article ID 260798, 17 pages, 2012.
- S. Guo and W. Jiang, “Hopf bifurcation analysis on general Gause-type predator-prey models with delay,” Abstract and Applied Analysis, vol. 2012, Article ID 363051, 17 pages, 2012.
- 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.
- N. H. Gazi and M. Bandyopadhyay, “Effect of time delay on a detritus-based ecosystem,” International Journal of Mathematics and Mathematical Sciences, vol. 2006, Article ID 25619, 28 pages, 2006.
- Y. Xue and X. Wang, “Stability and local Hopf bifurcation for a predator-prey model with delay,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 252437, 17 pages, 2012.
- Y. Bai and X. Zhang, “Stability and Hopf bifurcation in a diffusive predator-prey system with Beddington-DeAngelis functional response and time delay,” Abstract and Applied Analysis, vol. 2011, Article ID 463721, 22 pages, 2011.
- J.-F. Zhang, “Bifurcation analysis of a modified Holling-Tanner predator-prey model with time delay,” Applied Mathematical Modelling, vol. 36, no. 3, pp. 1219–1231, 2012.
- X. Li, S. Ruan, and J. Wei, “Stability and bifurcation in delay-differential equations with two delays,” Journal of Mathematical Analysis and Applications, vol. 236, no. 2, pp. 254–280, 1999.
- Y. Song, M. Han, and Y. Peng, “Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays,” Chaos, Solitons & Fractals, vol. 22, no. 5, pp. 1139–1148, 2004.
- S. Gakkhar and A. Singh, “Complex dynamics in a prey predator system with multiple delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 2, pp. 914–929, 2012.
- X.-Y. Meng, H.-F. Huo, X.-B. Zhang, and H. Xiang, “Stability and Hopf bifurcation in a three-species system with feedback delays,” Nonlinear Dynamics, vol. 64, no. 4, pp. 349–364, 2011.
- B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, Cambridge University Press, Cambridge, Mass, USA, 1981.
- T. K. Kar and A. Ghorai, “Dynamic behaviour of a delayed predator-prey model with harvesting,” Applied Mathematics and Computation, vol. 217, no. 22, pp. 9085–9104, 2011.