Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays
This paper is concerned with a computer virus model with two delays. Its dynamics are studied in terms of local stability and Hopf bifurcation. Sufficient conditions for local stability of the positive equilibrium and existence of the local Hopf bifurcation are obtained by regarding the possible com...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/560804 |
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| _version_ | 1832563639336304640 |
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| author | Zizhen Zhang Huizhong Yang |
| author_facet | Zizhen Zhang Huizhong Yang |
| author_sort | Zizhen Zhang |
| collection | DOAJ |
| description | This paper is concerned with a computer virus model with two delays. Its dynamics are studied in terms of local stability and Hopf bifurcation. Sufficient conditions for local stability of the
positive equilibrium and existence of the local Hopf bifurcation are obtained by regarding the possible combinations of the two delays as a bifurcation parameter. Furthermore, explicit formulae for determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are obtained by using the normal form method and center manifold theory. Finally, some numerical simulations are presented to support the theoretical results. |
| format | Article |
| id | doaj-art-6b07fbb228ec4680933c8ff2c796ba87 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6b07fbb228ec4680933c8ff2c796ba872025-02-03T01:13:00ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/560804560804Hopf Bifurcation Analysis for a Computer Virus Model with Two DelaysZizhen Zhang0Huizhong Yang1Key Laboratory of Advanced Process Control for Light Industry, Jiangnan University, Wuxi 214122, ChinaKey Laboratory of Advanced Process Control for Light Industry, Jiangnan University, Wuxi 214122, ChinaThis paper is concerned with a computer virus model with two delays. Its dynamics are studied in terms of local stability and Hopf bifurcation. Sufficient conditions for local stability of the positive equilibrium and existence of the local Hopf bifurcation are obtained by regarding the possible combinations of the two delays as a bifurcation parameter. Furthermore, explicit formulae for determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are obtained by using the normal form method and center manifold theory. Finally, some numerical simulations are presented to support the theoretical results.http://dx.doi.org/10.1155/2013/560804 |
| spellingShingle | Zizhen Zhang Huizhong Yang Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays Abstract and Applied Analysis |
| title | Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays |
| title_full | Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays |
| title_fullStr | Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays |
| title_full_unstemmed | Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays |
| title_short | Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays |
| title_sort | hopf bifurcation analysis for a computer virus model with two delays |
| url | http://dx.doi.org/10.1155/2013/560804 |
| work_keys_str_mv | AT zizhenzhang hopfbifurcationanalysisforacomputervirusmodelwithtwodelays AT huizhongyang hopfbifurcationanalysisforacomputervirusmodelwithtwodelays |