Stability and Bifurcation of Delayed Fractional-Order Dual Congestion Control Algorithms
In this technical note, fractional-order congestion control systems are introduced for the first time. In comparison with the conventional integer-order dual congestion control algorithms, the fractional control algorithms are more accurate and versatile. Bifurcation theory in fractional-order diffe...
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| Veröffentlicht in: | IEEE transactions on automatic control 2017-09, Vol.62 (9), p.4819-4826 |
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| creator | Xiao, Min Zheng, Wei Xing Jiang, Guoping Cao, Jinde |
| description | In this technical note, fractional-order congestion control systems are introduced for the first time. In comparison with the conventional integer-order dual congestion control algorithms, the fractional control algorithms are more accurate and versatile. Bifurcation theory in fractional-order differential equations is still an outstanding problem. Sufficient conditions for the occurrence of Hopf bifurcations are extended from integer-order dynamical systems to fractional-order cases. Then, these conditions are used to establish the existence of Hopf bifurcations for the delayed fractional-order model of dual congestion control algorithms proposed in this note. Finally, the onsets of bifurcations are identified, where Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Illustrative examples are also provided to demonstrate the theoretical results. |
| doi_str_mv | 10.1109/TAC.2017.2688583 |
| format | Article |
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In comparison with the conventional integer-order dual congestion control algorithms, the fractional control algorithms are more accurate and versatile. Bifurcation theory in fractional-order differential equations is still an outstanding problem. Sufficient conditions for the occurrence of Hopf bifurcations are extended from integer-order dynamical systems to fractional-order cases. Then, these conditions are used to establish the existence of Hopf bifurcations for the delayed fractional-order model of dual congestion control algorithms proposed in this note. Finally, the onsets of bifurcations are identified, where Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Illustrative examples are also provided to demonstrate the theoretical results.</description><subject>Bifurcation</subject><subject>Congestion control</subject><subject>Differential equations</subject><subject>fractional-order dynamical systems</subject><subject>Heuristic algorithms</subject><subject>hopf bifurcation</subject><subject>Mathematical model</subject><subject>Numerical stability</subject><subject>stability</subject><subject>Stability criteria</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kM1OwzAQhC0EEqVwR-LiF0jx2omzPpaUAlKlHigSt8hN1sXIbZCdHvr2pLTitD-aWc1-jN2DmAAI87iaVhMpoJxIjVigumAjKArMZCHVJRsJAZgZifqa3aT0PYw6z2HEPt97u_bB9wdudy1_8m4fG9v7bsc7x2cU7IFaPo-2Oe5syJaxpchnext41e02lP60Q9vHLvBp2HTR91_bdMuunA2J7s51zD7mz6vqNVssX96q6SJrFIg-00gOrJaulCZHR0MuaQ060FrK0lkQmgp0jqAE5YSGtVYGWpcTFWs1_Dlm4nS3iV1KkVz9E_3WxkMNoj6SqQcy9ZFMfSYzWB5OFk9E__ISEQ0a9QuXT1-u</recordid><startdate>201709</startdate><enddate>201709</enddate><creator>Xiao, Min</creator><creator>Zheng, Wei Xing</creator><creator>Jiang, Guoping</creator><creator>Cao, Jinde</creator><general>IEEE</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>201709</creationdate><title>Stability and Bifurcation of Delayed Fractional-Order Dual Congestion Control Algorithms</title><author>Xiao, Min ; Zheng, Wei Xing ; Jiang, Guoping ; Cao, Jinde</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c310t-68ef1a62f72948fe0162a98f166227fa106e58ffe1713f061b6391df4ee5b3583</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Bifurcation</topic><topic>Congestion control</topic><topic>Differential equations</topic><topic>fractional-order dynamical systems</topic><topic>Heuristic algorithms</topic><topic>hopf bifurcation</topic><topic>Mathematical model</topic><topic>Numerical stability</topic><topic>stability</topic><topic>Stability criteria</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xiao, Min</creatorcontrib><creatorcontrib>Zheng, Wei Xing</creatorcontrib><creatorcontrib>Jiang, Guoping</creatorcontrib><creatorcontrib>Cao, Jinde</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Xiao, Min</au><au>Zheng, Wei Xing</au><au>Jiang, Guoping</au><au>Cao, Jinde</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability and Bifurcation of Delayed Fractional-Order Dual Congestion Control Algorithms</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2017-09</date><risdate>2017</risdate><volume>62</volume><issue>9</issue><spage>4819</spage><epage>4826</epage><pages>4819-4826</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>In this technical note, fractional-order congestion control systems are introduced for the first time. In comparison with the conventional integer-order dual congestion control algorithms, the fractional control algorithms are more accurate and versatile. Bifurcation theory in fractional-order differential equations is still an outstanding problem. Sufficient conditions for the occurrence of Hopf bifurcations are extended from integer-order dynamical systems to fractional-order cases. Then, these conditions are used to establish the existence of Hopf bifurcations for the delayed fractional-order model of dual congestion control algorithms proposed in this note. Finally, the onsets of bifurcations are identified, where Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Illustrative examples are also provided to demonstrate the theoretical results.</abstract><pub>IEEE</pub><doi>10.1109/TAC.2017.2688583</doi><tpages>8</tpages></addata></record> |
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| subjects | Bifurcation Congestion control Differential equations fractional-order dynamical systems Heuristic algorithms hopf bifurcation Mathematical model Numerical stability stability Stability criteria |
| title | Stability and Bifurcation of Delayed Fractional-Order Dual Congestion Control Algorithms |
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