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Stability and Bifurcation of a Computer Virus Propagation Model with Delay and Incomplete Antivirus Ability

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  • Jianguo Ren
  • Yonghong Xu

Abstract

A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value . By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable if , whereas the virus equilibrium is globally asymptotically stable if . Numerical examples are presented to illustrate possible behavioral scenarios of the mode.

Suggested Citation

  • Jianguo Ren & Yonghong Xu, 2014. "Stability and Bifurcation of a Computer Virus Propagation Model with Delay and Incomplete Antivirus Ability," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-9, September.
    • Handle: RePEc:hin:jnlmpe:475934
    DOI: 10.1155/2014/475934
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