Dynamics of a Discrete Internet Congestion Control Model
We consider a discrete Internet model with a single link accessed by a single source, which responds to congestion signals from the network. Firstly, the stability of the equilibria of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation pa...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/628369 |
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| _version_ | 1832546564710596608 |
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| author | Yingguo Li |
| author_facet | Yingguo Li |
| author_sort | Yingguo Li |
| collection | DOAJ |
| description | We consider a discrete Internet model with a single link accessed by a single source, which responds to congestion signals from the network. Firstly, the stability of the equilibria of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Neimark-Sacker bifurcations occur when the delay passes a sequence of critical values. Then, the explicit algorithm for determining the direction of the Neimark-Sacker bifurcations and the stability of the bifurcating periodic solutions is derived. Finally, some numerical simulations are given to verify the theoretical analysis. |
| format | Article |
| id | doaj-art-e2035e199f1b4feaae8ae48ff26b0063 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e2035e199f1b4feaae8ae48ff26b00632025-02-03T06:48:17ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/628369628369Dynamics of a Discrete Internet Congestion Control ModelYingguo Li0School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, ChinaWe consider a discrete Internet model with a single link accessed by a single source, which responds to congestion signals from the network. Firstly, the stability of the equilibria of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Neimark-Sacker bifurcations occur when the delay passes a sequence of critical values. Then, the explicit algorithm for determining the direction of the Neimark-Sacker bifurcations and the stability of the bifurcating periodic solutions is derived. Finally, some numerical simulations are given to verify the theoretical analysis.http://dx.doi.org/10.1155/2011/628369 |
| spellingShingle | Yingguo Li Dynamics of a Discrete Internet Congestion Control Model Discrete Dynamics in Nature and Society |
| title | Dynamics of a Discrete Internet Congestion Control Model |
| title_full | Dynamics of a Discrete Internet Congestion Control Model |
| title_fullStr | Dynamics of a Discrete Internet Congestion Control Model |
| title_full_unstemmed | Dynamics of a Discrete Internet Congestion Control Model |
| title_short | Dynamics of a Discrete Internet Congestion Control Model |
| title_sort | dynamics of a discrete internet congestion control model |
| url | http://dx.doi.org/10.1155/2011/628369 |
| work_keys_str_mv | AT yingguoli dynamicsofadiscreteinternetcongestioncontrolmodel |