- 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
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 927369, 11 pages
Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model
1College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
2Key Laboratory of Medical Image Computing, Northeastern University, Ministry of Education, Shenyang 110819, China
Received 18 January 2013; Revised 4 August 2013; Accepted 26 August 2013
Academic Editor: Yannick De Decker
Copyright © 2013 Yu Yao 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.
- N. Yoshida and T. Hara, “Global stability of a delayed SIR epidemic model with density dependent birth and death rates,” Journal of Computational and Applied Mathematics, vol. 201, no. 2, pp. 339–347, 2007.
- M. Song, W. Ma, and Y. Takeuchi, “Permanence of a delayed SIR epidemic model with density dependent birth rate,” Journal of Computational and Applied Mathematics, vol. 201, no. 2, pp. 389–394, 2007.
- J. Liu and T. Zhang, “Bifurcation analysis of an SIS epidemic model with nonlinear birth rate,” Chaos, Solitons and Fractals, vol. 40, no. 3, pp. 1091–1099, 2009.
- V. Yegneswaran, P. Barford, and D. Plonka, “On the design and use of internet sinks for network abuse monitoring,” Computer Science, vol. 3224, pp. 146–165, 2004.
- D. Yeung and Y. Ding, “Host-based intrusion detection using dynamic and static behavioral models,” Pattern Recognition, vol. 36, no. 1, pp. 229–243, 2003.
- N. Stakhanova, S. Basu, and J. Wong, “On the symbiosis of specification-based and anomaly-based detection,” Computers and Security, vol. 29, no. 2, pp. 253–268, 2010.
- G. P. Spathoulas and S. K. Katsikas, “Reducing false positives in intrusion detection systems,” Computers and Security, vol. 29, no. 1, pp. 35–44, 2010.
- C. Lin, B. Liu, H. Hu, F. Xiao, and J. Zhang, “Detecting hidden Malware method based on “In-VM” model,” China Communications, vol. 8, no. 4, pp. 99–108, 2011.
- S. Staniford, V. Paxson, and N. Weaver, “How to own the internet in your spare time,” in Proceedings of the 11th USENIX Security Symposium, pp. 149–167, San Francisco, Calif, USA, 2002.
- S. Qing and W. Wen, “A survey and trends on Internet worms,” Computers and Security, vol. 24, no. 4, pp. 334–346, 2005.
- C. C. Zou, W. Gong, and D. Towsley, “Worm propagation modeling and analysis under dynamic quarantine defense,” in Proceedings of the 2003 ACM Workshop on Rapid Malcode (WORM '03), pp. 51–60, Washington, DC, USA, October 2003.
- J. Ren, X. Yang, Q. Zhu, L. Yang, and C. Zhang, “A novel computer virus model and its dynamics,” Nonlinear Analysis: Real World Applications, vol. 13, no. 1, pp. 376–384, 2012.
- B. K. Mishra and S. K. Pandey, “Fuzzy epidemic model for the transmission of worms in computer network,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 4335–4341, 2010.
- L.-X. Yang and X. Yang, “Propagation behavior of virus codes in the situation that infected computers are connected to the internet with positive probability,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 693695, 13 pages, 2012.
- Y. Yao, X. Xie, H. Guo, G. Yu, F. Gao, and X. Tong, “Hopf bifurcation in an Internet worm propagation model with time delay in quarantine,” Mathematical and Computer Modelling, 2011.
- Y. Yao, W. Xiang, A. Qu, G. Yu, and F. Gao, “Hopf bifurcation in an SEIDQV worm propagation model with quarantine strategy,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 304868, 18 pages, 2012.
- Y. Yao, L. Guo, H. Guo, G. Yu, F. Gao, and X. Tong, “Pulse quarantine strategy of internet worm propagation: modeling and analysis,” Computers and Electrical Engineering, 2011.
- F. Wang, Y. Zhang, C. Wang, J. Ma, and S. Moon, “Stability analysis of a SEIQV epidemic model for rapid spreading worms,” Computers and Security, vol. 29, no. 4, pp. 410–418, 2010.
- T. Dong, X. Liao, and H. Li, “Stability and Hopf bifurcation in a computer virus model with multistate antivirus,” Abstract and Applied Analysis, vol. 2012, Article ID 841987, 16 pages, 2012.
- T. Zhang, J. Liu, and Z. Teng, “Stability of Hopf bifurcation of a delayed SIRS epidemic model with stage structure,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 293–306, 2010.
- J. Zhang, W. Li, and X. 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.
- W. Kermack and A. McKendrick, “A contribution to the mathematical theory of epidemics,” Proceedings of the Royal Society of London A, vol. 115, no. 772, pp. 700–721, 1927.
- S. Wang, Q. Liu, X. Yu, and Y. Ma, “Bifurcation analysis of a model for network worm propagation with time delay,” Mathematical and Computer Modelling, vol. 52, no. 3-4, pp. 435–447, 2010.
- B. Hassard, D. Kazarino, and Y. Wan, Theory and Application of Hopf Bifurcation, Cambridge University Press, Cambridge, UK, 1981.