Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network
We drive a scalar delay differential system to model the congestion of a wireless access network setting. The Hopf bifurcation of this system is investigated using the control and bifurcation theory; it is proved that there exists a critical value of delay for the stability. When the delay value pas...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/632564 |
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| _version_ | 1832566573253001216 |
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| author | Wen-bo Zhao Xiao-ke Sun Huicheng Wang |
| author_facet | Wen-bo Zhao Xiao-ke Sun Huicheng Wang |
| author_sort | Wen-bo Zhao |
| collection | DOAJ |
| description | We drive a scalar delay differential system to model the congestion of a wireless access network setting. The Hopf bifurcation of this system is investigated using the control and bifurcation theory; it is proved that there exists a critical value of delay for the stability. When the delay value passes through the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. Finally, some examples and numerical simulations are presented to show the feasibility of the theoretical results. |
| format | Article |
| id | doaj-art-cbdcd30d6416439a927234c63f788fc7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-cbdcd30d6416439a927234c63f788fc72025-02-03T01:03:47ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/632564632564Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access NetworkWen-bo Zhao0Xiao-ke Sun1Huicheng Wang2School of Physics and Information, Tianshui Normal University, Tianshui, Gansu 741000, ChinaSchool of Mathematics and Statistics, Tianshui Normal University, Tianshui, Gansu 741000, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, ChinaWe drive a scalar delay differential system to model the congestion of a wireless access network setting. The Hopf bifurcation of this system is investigated using the control and bifurcation theory; it is proved that there exists a critical value of delay for the stability. When the delay value passes through the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. Finally, some examples and numerical simulations are presented to show the feasibility of the theoretical results.http://dx.doi.org/10.1155/2014/632564 |
| spellingShingle | Wen-bo Zhao Xiao-ke Sun Huicheng Wang Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network Abstract and Applied Analysis |
| title | Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network |
| title_full | Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network |
| title_fullStr | Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network |
| title_full_unstemmed | Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network |
| title_short | Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network |
| title_sort | hopf bifurcation and stability analysis of a congestion control model with delay in wireless access network |
| url | http://dx.doi.org/10.1155/2014/632564 |
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