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Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence

Author

Listed:
  • Zizhen Zhang
  • Yougang Wang
  • Luca Guerrini

Abstract

This paper is concerned with a delayed SVEIR worm propagation model with saturated incidence. The main objective is to investigate the effect of the time delay on the model. Sufficient conditions for local stability of the positive equilibrium and existence of a Hopf bifurcation are obtained by choosing the time delay as the bifurcation parameter. Particularly, explicit formulas determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold theorem. Numerical simulations for a set of parameter values are carried out to illustrate the analytical results.

Suggested Citation

  • Zizhen Zhang & Yougang Wang & Luca Guerrini, 2018. "Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence," Advances in Mathematical Physics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:7619074
    DOI: 10.1155/2018/7619074
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    References listed on IDEAS

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    1. Keshri, Neha & Mishra, Bimal Kumar, 2014. "Two time-delay dynamic model on the transmission of malicious signals in wireless sensor network," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 151-158.
    2. 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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