Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay
A computer virus model with infection delay and recovery delay is considered. The sufficient conditions for the global stability of the virus infection equilibrium are established. We show that the time delay can destabilize the virus infection equilibrium and give rise to Hopf bifurcations and stab...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/929580 |
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| _version_ | 1849304510183243776 |
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| author | Haitao Song Qiaochu Wang Weihua Jiang |
| author_facet | Haitao Song Qiaochu Wang Weihua Jiang |
| author_sort | Haitao Song |
| collection | DOAJ |
| description | A computer virus model with infection delay and recovery delay is considered. The sufficient conditions for the global stability of the virus infection equilibrium are established. We show that the time delay can destabilize the virus infection equilibrium and give rise to Hopf bifurcations and stable periodic orbits. By the normal form and center manifold theory, the direction of the Hopf bifurcation and stability of the bifurcating periodic orbits are determined. Numerical simulations are provided to support our theoretical conclusions. |
| format | Article |
| id | doaj-art-420034e00ba6494ab7e64dafbbbee0ab |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-420034e00ba6494ab7e64dafbbbee0ab2025-08-20T03:55:43ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/929580929580Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery DelayHaitao Song0Qiaochu Wang1Weihua Jiang2Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Architecture, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaA computer virus model with infection delay and recovery delay is considered. The sufficient conditions for the global stability of the virus infection equilibrium are established. We show that the time delay can destabilize the virus infection equilibrium and give rise to Hopf bifurcations and stable periodic orbits. By the normal form and center manifold theory, the direction of the Hopf bifurcation and stability of the bifurcating periodic orbits are determined. Numerical simulations are provided to support our theoretical conclusions.http://dx.doi.org/10.1155/2014/929580 |
| spellingShingle | Haitao Song Qiaochu Wang Weihua Jiang Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay Journal of Applied Mathematics |
| title | Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay |
| title_full | Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay |
| title_fullStr | Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay |
| title_full_unstemmed | Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay |
| title_short | Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay |
| title_sort | stability and hopf bifurcation of a computer virus model with infection delay and recovery delay |
| url | http://dx.doi.org/10.1155/2014/929580 |
| work_keys_str_mv | AT haitaosong stabilityandhopfbifurcationofacomputervirusmodelwithinfectiondelayandrecoverydelay AT qiaochuwang stabilityandhopfbifurcationofacomputervirusmodelwithinfectiondelayandrecoverydelay AT weihuajiang stabilityandhopfbifurcationofacomputervirusmodelwithinfectiondelayandrecoverydelay |