- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 705601, 8 pages
Bifurcation and Chaotic Behavior of a Discrete-Time SIS Model
Department of Mathematics and Sciences, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou, Hebei 075000, China
Received 5 January 2013; Accepted 8 April 2013
Academic Editor: Qingdu Li
Copyright © 2013 Junhong Li and Ning Cui. 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.
- L. Cai, X. Li, M. Ghosh, and B. Guo, “Stability analysis of an HIV/AIDS epidemic model with treatment,” Journal of Computational and Applied Mathematics, vol. 229, no. 1, pp. 313–323, 2009.
- Y.-H. Hsieh, C.-C. King, C. W. S. Chen, M.-S. Ho, S.-B. Hsu, and Y.-C. Wu, “Impact of quarantine on the 2003 SARS outbreak: a retrospective modeling study,” Journal of Theoretical Biology, vol. 244, no. 4, pp. 729–736, 2007.
- S. Iwami, Y. Takeuchi, X. Liu, and S. Nakaoka, “A geographical spread of vaccine-resistance in avian influenza epidemics,” Journal of Theoretical Biology, vol. 259, no. 2, pp. 219–228, 2009.
- D. Summers, J. G. Cranford, and B. P. Healey, “Chaos in periodically forced discrete-time ecosystem models,” Chaos, Solitons and Fractals, vol. 11, no. 14, pp. 2331–2342, 2000.
- J. Vandermeer, L. Stone, and B. Blasius, “Categories of chaos and fractal basin boundaries in forced predator-prey models,” Chaos, Solitons and Fractals, vol. 12, no. 2, pp. 265–276, 2001.
- A. Gray, D. Greenhalgh, X. Mao, and J. Pan, “The SIS epidemic model with Markovian switching,” Journal of Mathematical Analysis and Applications, vol. 394, no. 2, pp. 496–516, 2012.
- A. Gray, D. Greenhalgh, L. Hu, X. Mao, and J. Pan, “A stochastic differential equation SIS epidemic model,” SIAM Journal on Applied Mathematics, vol. 71, no. 3, pp. 876–902, 2011.
- J. Liu and T. Zhang, “Bifurcation analysis of an SIS epidemic model with nonlinear birth rate,” Chaos, Solitons & Fractals, vol. 40, no. 3, pp. 1091–1099, 2009.
- D. Gao and S. Ruan, “An SIS patch model with variable transmission coefficients,” Mathematical Biosciences, vol. 232, no. 2, pp. 110–115, 2011.
- Y. Li and J. Cui, “The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2353–2365, 2009.
- Q. Wu and X. Fu, “Modelling of discrete-time SIS models with awareness interactions on degree-uncorrelated networks,” Physica A, vol. 390, no. 3, pp. 463–470, 2011.
- P. L. Salceanu and H. L. Smith, “Persistence in a discrete-time stage-structured fungal disease model,” Journal of Biological Dynamics, vol. 3, no. 2-3, pp. 271–285, 2009.
- J. E. Franke and A.-A. Yakubu, “Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models,” Journal of Mathematical Biology, vol. 57, no. 6, pp. 755–790, 2008.
- J. Li, Z. Ma, and F. Brauer, “Global analysis of discrete-time SI and SIS epidemic models,” Mathematical Biosciences and Engineering, vol. 4, no. 4, pp. 699–710, 2007.
- L. J. S. Allen, Y. Lou, and A. L. Nevai, “Spatial patterns in a discrete-time SIS patch model,” Journal of Mathematical Biology, vol. 58, no. 3, pp. 339–375, 2009.
- L. Li, G.-Q. Sun, and Z. Jin, “Bifurcation and chaos in an epidemic model with nonlinear incidence rates,” Applied Mathematics and Computation, vol. 216, no. 4, pp. 1226–1234, 2010.
- J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, vol. 42, Springer, New York, NY, USA, 1983.
- S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, vol. 2, Springer, New York, NY, USA, 1990.
- T. Chen, J. He, and Q. Yin, “Dynamics evolution of credit risk contagion in the CRT market,” Dynamics in Nature and Society, vol. 2013, Article ID 206201, 9 pages, 2013.
- Q. Li, L. Zhang, and F. Yang, “An algorithm to automatically detect the Smale horseshoes,” Discrete Dynamics in Nature and Society, Article ID 283179, 9 pages, 2012.
- Q. Li and X.-S. Yang, “A simple method for finding topological horseshoes,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 20, no. 2, pp. 467–478, 2010.
- X.-S. Yang, “Topological horseshoes and computer assisted verification of chaotic dynamics,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 19, no. 4, pp. 1127–1145, 2009.
- L. Qingdu and T. Song, “Algorithm for finding horseshoes in three-dimensinal hyperchaltic maps and its application,” Acta Physica Sinica, vol. 62, no. 2, Article ID 020510, 2013.
- M. P. Hassell, H. N. Comins, and R. M. May, “Spatial structure and chaos in insect population dynamics,” Nature, vol. 353, pp. 255–258, 1991.
- A. A. Berryman and J. A. Millstein, “Are ecological systems chaotic and if not, why not?” Trends in Ecology & Evolution, vol. 4, no. 1, pp. 26–28, 1989.