Hopf bifurcation analysis of a delayed viral infection model in computer networks

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• 作者：Liping Feng^a ; ^b ; ^{fenglp@yeah.net} ; Xiaofeng Liao^a ; ^{xfliao@cqu.edu.cn} ; Huaqing Li^a ; ^{lhq_jsack@126.com} ; Qi Han^a ; ^{yiding1981@yahoo.com.cn}
• 关键词：Computer virus ; Hopf bifurcation ; Stability ; Virus model ; Time delay
• 刊名：Mathematical and Computer Modelling
• 出版年：2012
• 期刊代码：86_08957177
• 类别：cp
• 出版时间：October, 2012
• 卷：56
• 期：7-8
• 页码：167-179
• 文件大小：1079 K

摘要

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.