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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 927369, 11 pages
Research Article

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.


A delayed worm propagation model with birth and death rates is formulated. The stability of the positive equilibrium is studied. Through theoretical analysis, a critical value of Hopf bifurcation is derived. The worm propagation system is locally asymptotically stable when time delay is less than . However, Hopf bifurcation appears when time delay passes the threshold , which means that the worm propagation system is unstable and out of control. Consequently, time delay should be adjusted to be less than to ensure the stability of the system stable and better prediction of the scale and speed of Internet worm spreading. Finally, numerical and simulation experiments are presented to simulate the system, which fully support our analysis.