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Dynamical Analysis of a Computer Virus Model with Delays

Author

Listed:
  • Juan Liu
  • Carlo Bianca
  • Luca Guerrini

Abstract

An SIQR computer virus model with two delays is investigated in the present paper. The linear stability conditions are obtained by using characteristic root method and the developed asymptotic analysis shows the onset of a Hopf bifurcation occurs when the delay parameter reaches a critical value. Moreover the direction of the Hopf bifurcation and stability of the bifurcating period solutions are investigated by using the normal form theory and the center manifold theorem. Finally, numerical investigations are carried out to show the feasibility of the theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:5649584
    DOI: 10.1155/2016/5649584
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    References listed on IDEAS

    as
    1. Massimiliano Ferrara & Luca Guerrini & Giovanni Molica Bisci, 2013. "Center Manifold Reduction and Perturbation Method in a Delayed Model with a Mound‐Shaped Cobb‐Douglas Production Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Tao Dong & Xiaofeng Liao & Huaqing Li, 2012. "Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, April.
    3. Massimiliano Ferrara & Luca Guerrini & Giovanni Molica Bisci, 2013. "Center Manifold Reduction and Perturbation Method in a Delayed Model with a Mound-Shaped Cobb-Douglas Production Function," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, December.
    4. repec:plo:pone00:0134507 is not listed on IDEAS
    5. 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).
    6. Ren, Jianguo & Yang, Xiaofan & Yang, Lu-Xing & Xu, Yonghong & Yang, Fanzhou, 2012. "A delayed computer virus propagation model and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 74-79.
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