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Bifurcation analysis of a model for network worm propagation with time delay. (English) Zbl 1201.68060
Summary: Considering that reassembly of a system and/or using anti-virus software will take a period of time, we introduce a time delay for modeling this period of time. Also, considering that at different times the propagation of a worm shows different characteristics, we build a section model for Internet worm propagation depending on a two-factor model. We first consider the stability of the positive equilibrium and the existence of a local Hopf bifurcation. In succession, using the normal form theory and center manifold argument, we derive explicit formulas determining the stability, direction and other properties of bifurcation periodic solutions. Finally, a numerical simulation is presented. The techniques of analysis of the mathematical model provide a theoretical foundation for control and forecasting for Internet worms.

68Q25Analysis of algorithms and problem complexity
68M11Internet topics
34K18Bifurcation theory of functional differential equations
34K20Stability theory of functional-differential equations
Full Text: DOI
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