Dynamical Analysis of a Viral Infection Model with Delays in Computer Networks

Dynamical Analysis of a Viral Infection Model with Delays in Computer Networks

This paper is devoted to the study of an SIRS computer virus propagation model with two delays and multistate antivirus measures. We demonstrate that the system loses its stability and a Hopf bifurcation occurs when the delay passes through the corresponding critical value by choosing the possible c...

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Main Authors: Zizhen Zhang, Huizhong Yang
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2015/280856
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spelling doaj-8cea291eb2304c12a8294e5108a3ec132020-11-24T22:54:25ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/280856280856Dynamical Analysis of a Viral Infection Model with Delays in Computer NetworksZizhen Zhang0Huizhong Yang1School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, ChinaKey Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, ChinaThis paper is devoted to the study of an SIRS computer virus propagation model with two delays and multistate antivirus measures. We demonstrate that the system loses its stability and a Hopf bifurcation occurs when the delay passes through the corresponding critical value by choosing the possible combination of the two delays as the bifurcation parameter. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by means of the center manifold theorem and the normal form theory. Finally, some numerical simulations are performed to illustrate the obtained results.http://dx.doi.org/10.1155/2015/280856
collection DOAJ
language English
format Article
sources DOAJ
author Zizhen Zhang
Huizhong Yang
spellingShingle Zizhen Zhang
Huizhong Yang
Dynamical Analysis of a Viral Infection Model with Delays in Computer Networks
Mathematical Problems in Engineering
author_facet Zizhen Zhang
Huizhong Yang
author_sort Zizhen Zhang
title Dynamical Analysis of a Viral Infection Model with Delays in Computer Networks
title_short Dynamical Analysis of a Viral Infection Model with Delays in Computer Networks
title_full Dynamical Analysis of a Viral Infection Model with Delays in Computer Networks
title_fullStr Dynamical Analysis of a Viral Infection Model with Delays in Computer Networks
title_full_unstemmed Dynamical Analysis of a Viral Infection Model with Delays in Computer Networks
title_sort dynamical analysis of a viral infection model with delays in computer networks
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2015-01-01
description This paper is devoted to the study of an SIRS computer virus propagation model with two delays and multistate antivirus measures. We demonstrate that the system loses its stability and a Hopf bifurcation occurs when the delay passes through the corresponding critical value by choosing the possible combination of the two delays as the bifurcation parameter. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by means of the center manifold theorem and the normal form theory. Finally, some numerical simulations are performed to illustrate the obtained results.
url http://dx.doi.org/10.1155/2015/280856
work_keys_str_mv AT zizhenzhang dynamicalanalysisofaviralinfectionmodelwithdelaysincomputernetworks
AT huizhongyang dynamicalanalysisofaviralinfectionmodelwithdelaysincomputernetworks
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