Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model
A delayed worm propagation model with birth and death rates is formulated. The stability of the positive equilibrium is studied. Through theoretical analysis, a critical value τ0 of Hopf bifurcation is derived. The worm propagation system is locally asymptotically stable when time delay is less than...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/927369 |
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| _version_ | 1832556777285091328 |
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| author | Yu Yao Nan Zhang Wenlong Xiang Ge Yu Fuxiang Gao |
| author_facet | Yu Yao Nan Zhang Wenlong Xiang Ge Yu Fuxiang Gao |
| author_sort | Yu Yao |
| collection | DOAJ |
| description | A delayed worm propagation model with birth and death rates is formulated. The stability of the positive equilibrium is studied. Through theoretical analysis, a critical value τ0 of Hopf bifurcation is derived. The worm propagation system is locally asymptotically stable when time delay is less than τ0. However, Hopf bifurcation appears when time delay τ passes the threshold τ0, which means that the worm propagation system is unstable and out of control. Consequently, time delay should be adjusted to be less than τ0 to ensure the stability of the system stable and better prediction of the scale and speed of Internet worm spreading. Finally, numerical and simulation experiments are presented to simulate the system, which fully support our analysis. |
| format | Article |
| id | doaj-art-dc8d9bbaa22d4e7bb977aa1cc7c53646 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-dc8d9bbaa22d4e7bb977aa1cc7c536462025-02-03T05:44:31ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/927369927369Modeling and Analysis of Bifurcation in a Delayed Worm Propagation ModelYu Yao0Nan Zhang1Wenlong Xiang2Ge Yu3Fuxiang Gao4College of Information Science and Engineering, Northeastern University, Shenyang 110819, ChinaCollege of Information Science and Engineering, Northeastern University, Shenyang 110819, ChinaCollege of Information Science and Engineering, Northeastern University, Shenyang 110819, ChinaCollege of Information Science and Engineering, Northeastern University, Shenyang 110819, ChinaCollege of Information Science and Engineering, Northeastern University, Shenyang 110819, ChinaA delayed worm propagation model with birth and death rates is formulated. The stability of the positive equilibrium is studied. Through theoretical analysis, a critical value τ0 of Hopf bifurcation is derived. The worm propagation system is locally asymptotically stable when time delay is less than τ0. However, Hopf bifurcation appears when time delay τ passes the threshold τ0, which means that the worm propagation system is unstable and out of control. Consequently, time delay should be adjusted to be less than τ0 to ensure the stability of the system stable and better prediction of the scale and speed of Internet worm spreading. Finally, numerical and simulation experiments are presented to simulate the system, which fully support our analysis.http://dx.doi.org/10.1155/2013/927369 |
| spellingShingle | Yu Yao Nan Zhang Wenlong Xiang Ge Yu Fuxiang Gao Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model Journal of Applied Mathematics |
| title | Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model |
| title_full | Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model |
| title_fullStr | Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model |
| title_full_unstemmed | Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model |
| title_short | Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model |
| title_sort | modeling and analysis of bifurcation in a delayed worm propagation model |
| url | http://dx.doi.org/10.1155/2013/927369 |
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