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2013 Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model
Yu Yao, Nan Zhang, Wenlong Xiang, Ge Yu, Fuxiang Gao
J. Appl. Math. 2013(SI06): 1-11 (2013). DOI: 10.1155/2013/927369


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 τ0 of Hopf bifurcation is derived. The worm propagation system is locally asymptotically stable when time delay is less than τ0. However, Hopf bifurcation appears when time delay τ passes the threshold τ0, which means that the worm propagation system is unstable and out of control. Consequently, time delay should be adjusted to be less than τ0 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.


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Yu Yao. Nan Zhang. Wenlong Xiang. Ge Yu. Fuxiang Gao. "Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model." J. Appl. Math. 2013 (SI06) 1 - 11, 2013.


Published: 2013
First available in Project Euclid: 7 May 2014

zbMATH: 06950939
MathSciNet: MR3115289
Digital Object Identifier: 10.1155/2013/927369

Rights: Copyright © 2013 Hindawi


Vol.2013 • No. SI06 • 2013
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