Journal
MATHEMATICAL AND COMPUTER MODELLING
Volume 52, Issue 3-4, Pages 435-447Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.mcm.2010.02.044
Keywords
Network worm; Mathematical model; Time delay; Bifurcation analysis; Stability
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In this paper, 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. (C) 2010 Elsevier Ltd. All rights reserved.
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