- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 704320, 11 pages
Hopf Bifurcation Control in a Delayed Predator-Prey System with Prey Infection and Modified Leslie-Gower Scheme
1Key Laboratory of Advanced Process Control for Light Industry of the Ministry of Education, Jiangnan University, Wuxi 214122, China
2School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China
Received 9 May 2013; Accepted 4 June 2013
Academic Editor: Luca Guerrini
Copyright © 2013 Zizhen Zhang and Huizhong Yang. 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. Mukherjee, “Stability analysis of a stochastic model for prey-predator system with disease in the prey,” Lithuanian Association of Nonlinear Analysis (LANA), vol. 8, no. 2, pp. 83–92, 2003.
- M. Y. Li, J. R. Graef, L. Wang, and J. Karsai, “Global dynamics of a SEIR model with varying total population size,” Mathematical Biosciences, vol. 160, no. 2, pp. 191–213, 1999.
- Y. Xiao and L. Chen, “Analysis of a three species eco-epidemiological model,” Journal of Mathematical Analysis and Applications, vol. 258, no. 2, pp. 733–754, 2001.
- C. Sun, Y. Lin, and M. Han, “Stability and Hopf bifurcation for an epidemic disease model with delay,” Chaos, Solitons & Fractals, vol. 30, no. 1, pp. 204–216, 2006.
- J.-F. Zhang, W.-T. Li, and X.-P. Yan, “Hopf bifurcation and stability of periodic solutions in a delayed eco-epidemiological system,” Applied Mathematics and Computation, vol. 198, no. 2, pp. 865–876, 2008.
- S. Chakraborty, S. Pal, and N. Bairagi, “Dynamics of a ratio-dependent eco-epidemiological system with prey harvesting,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 1862–1877, 2010.
- X. Shi, J. Cui, and X. Zhou, “Stability and Hopf bifurcation analysis of an eco-epidemic model with a stage structure,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 4, pp. 1088–1106, 2011.
- W. O. Kermack and A. G. McKendrick, “A contribution to the mathematical theory of epidemics,” Proceedings of the Royal Society of London A, vol. 115, pp. 700–721, 1927.
- J. Chattopadhyay and O. Arino, “A predator-prey model with disease in the prey,” Nonlinear Analysis: Theory, Methods & Applications, vol. 36, no. 6, pp. 747–766, 1999.
- X. Zhou, J. Cui, X. Shi, and X. Song, “A modified Leslie-Gower predator-prey model with prey infection,” Journal of Applied Mathematics and Computing, vol. 33, no. 1-2, pp. 471–487, 2010.
- H. Guo and X. Song, “An impulsive predator-prey system with modified Leslie-Gower and Holling type II schemes,” Chaos, Solitons & Fractals, vol. 36, no. 5, pp. 1320–1331, 2008.
- Y. Zhu and K. Wang, “Existence and global attractivity of positive periodic solutions for a predator-prey model with modified Leslie-Gower Holling-type II schemes,” Journal of Mathematical Analysis and Applications, vol. 384, no. 2, pp. 400–408, 2011.
- X. Song and Y. Li, “Dynamic behaviors of the periodic predator-prey model with modified Leslie-Gower Holling-type II schemes and impulsive effect,” Nonlinear Analysis: Real World Applications, vol. 9, no. 1, pp. 64–79, 2008.
- L. Nie, Z. Teng, L. Hu, and J. Peng, “Qualitative analysis of a modified Leslie-Gower and Holling-type II predator-prey model with state dependent impulsive effects,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 1364–1373, 2010.
- G.-P. Hu and X.-L. Li, “Stability and Hopf bifurcation for a delayed predator-prey model with disease in the prey,” Chaos, Solitons & Fractals, vol. 45, no. 3, pp. 229–237, 2012.
- X. Zhou, X. Shi, and X. Song, “Analysis of a delay prey-predator model with disease in the prey species only,” Journal of the Korean Mathematical Society, vol. 46, no. 4, pp. 713–731, 2009.
- X. Zhou, X. Shi, and X. Song, “The dynamics of an eco-epidemiological model with distributed delay,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 4, pp. 685–699, 2009.
- S. Ruan and J. Wei, “On the zeros of transcendental functions with applications to stability of delay differential equations with two delays,” Dynamics of Continuous, Discrete & Impulsive Systems A, vol. 10, no. 6, pp. 863–874, 2003.
- B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, vol. 41 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, Mass, USA, 1981.