Journal
MATHEMATICAL AND COMPUTER MODELLING
Volume 56, Issue 7-8, Pages 167-179Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.mcm.2011.12.010
Keywords
Computer virus; Hopf bifurcation; Stability; Virus model; Time delay
Categories
Funding
- Fundamental Research Funds for the Central Universities [CDJXS11182239]
- National Natural Science Foundation of China [60973114, 60903213, 61003247]
- Natural Science Foundation of Chongqing (CSTC) [2008BB2189, 2009BA2024]
- Scientific Research Foundation of State Key Lab. of Power Transmission Equipment and System Security [2007DA10512711206]
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In this paper, a novel computer virus propagation model with dual delays and multi-state antivirus measures is considered. Using theories of stability and bifurcation, it is proven that there exists a critical value of delay for the stability of virus prevalence. When the delay exceeds the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the explicit formulas determining the stability and direction of bifurcating periodic solutions are obtained by applying the center manifold theorem and the normal form theory. Finally, some numerical simulations are performed to verify the theoretical analysis. The conclusions of this paper can contribute to a better theoretical basis for understanding the long-term actions of virus propagation in networks. (c) 2011 Elsevier Ltd. All rights reserved.
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