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Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus

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  • Tao Dong
  • Xiaofeng Liao
  • Huaqing Li

Abstract

By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti‐virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes through a sequence of critical value. The linerized model and stability of the bifurcating periodic solutions are also derived by applying the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.

Suggested Citation

  • Tao Dong & Xiaofeng Liao & Huaqing Li, 2012. "Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:841987
    DOI: 10.1155/2012/841987
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    References listed on IDEAS

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    1. Li, Xiuling & Wei, Junjie, 2005. "On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 519-526.
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    Cited by:

    1. Tao Dong & Xiaofeng Liao, 2013. "On the General Consensus Protocol in Multiagent Networks with Double‐Integrator Dynamics and Coupling Time Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Zizhen Zhang & Huizhong Yang, 2013. "Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Juan Liu, 2014. "Hopf Bifurcation in a Delayed SEIQRS Model for the Transmission of Malicious Objects in Computer Network," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    4. Yu Yao & Nan Zhang & Wenlong Xiang & Ge Yu & Fuxiang Gao, 2013. "Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. Juan Liu & Carlo Bianca & Luca Guerrini, 2016. "Dynamical Analysis of a Computer Virus Model with Delays," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    6. Haitao Song & Qiaochu Wang & Weihua Jiang, 2014. "Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    7. Chenquan Gan & Xiaofan Yang & Qingyi Zhu, 2014. "Global Stability of a Computer Virus Propagation Model with Two Kinds of Generic Nonlinear Probabilities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. Zizhen Zhang & Limin Song, 2017. "Dynamics of a Computer Virus Propagation Model with Delays and Graded Infection Rate," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    9. Wei Zhang & Xiaofan Yang & Luxing Yang, 2025. "A Delayed Malware Propagation Model Under a Distributed Patching Mechanism: Stability Analysis," Mathematics, MDPI, vol. 13(14), pages 1-31, July.

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