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Volume 34, Issue 3
Hopf Bifurcation of a Nonresident Computer Virus Model with Delay

Zizhen Zhang, Yougang Wang & Massimiliano Ferrara

Anal. Theory Appl., 34 (2018), pp. 199-208.

Published online: 2018-11

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  • Abstract

In this paper, a delayed nonresident computer virus model with graded infection rate is considered in which the following assumption is imposed: latent computers have lower infection ability than infectious computers. With the aid of the bifurcation theory, sufficient conditions for stability of the infected equilibrium of the model and existence of the Hopf bifurcation are established. In particular, explicit formulae which determine direction and stability of the Hopf bifurcation are derived by means of the normal form theory and the center manifold reduction for functional differential equations. Finally, a numerical example is given in order to show the feasibility of the obtained theoretical findings.

  • AMS Subject Headings

34C15, 34C23, 37G15, 37N25

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COPYRIGHT: © Global Science Press

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@Article{ATA-34-199, author = {Zizhen Zhang, Yougang Wang and Massimiliano Ferrara}, title = {Hopf Bifurcation of a Nonresident Computer Virus Model with Delay}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {3}, pages = {199--208}, abstract = {

In this paper, a delayed nonresident computer virus model with graded infection rate is considered in which the following assumption is imposed: latent computers have lower infection ability than infectious computers. With the aid of the bifurcation theory, sufficient conditions for stability of the infected equilibrium of the model and existence of the Hopf bifurcation are established. In particular, explicit formulae which determine direction and stability of the Hopf bifurcation are derived by means of the normal form theory and the center manifold reduction for functional differential equations. Finally, a numerical example is given in order to show the feasibility of the obtained theoretical findings.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2016-0035}, url = {http://global-sci.org/intro/article_detail/ata/12835.html} }
TY - JOUR T1 - Hopf Bifurcation of a Nonresident Computer Virus Model with Delay AU - Zizhen Zhang, Yougang Wang & Massimiliano Ferrara JO - Analysis in Theory and Applications VL - 3 SP - 199 EP - 208 PY - 2018 DA - 2018/11 SN - 34 DO - http://doi.org/10.4208/ata.OA-2016-0035 UR - https://global-sci.org/intro/article_detail/ata/12835.html KW - Computer virus, delay, Hopf bifurcation, SLA model, Periodic solution. AB -

In this paper, a delayed nonresident computer virus model with graded infection rate is considered in which the following assumption is imposed: latent computers have lower infection ability than infectious computers. With the aid of the bifurcation theory, sufficient conditions for stability of the infected equilibrium of the model and existence of the Hopf bifurcation are established. In particular, explicit formulae which determine direction and stability of the Hopf bifurcation are derived by means of the normal form theory and the center manifold reduction for functional differential equations. Finally, a numerical example is given in order to show the feasibility of the obtained theoretical findings.

Zizhen Zhang, Yougang Wang and Massimiliano Ferrara. (2018). Hopf Bifurcation of a Nonresident Computer Virus Model with Delay. Analysis in Theory and Applications. 34 (3). 199-208. doi:10.4208/ata.OA-2016-0035
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