{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:39:02Z","timestamp":1772293142488,"version":"3.50.1"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,8]]},"abstract":"<jats:p>In this note, we consider Hopf bifurcation control for an Internet congestion model with a single route accessed by a single source. It has been shown that the system without control cannot guarantee a stationary sending rate. As the positive gain parameter of the system passes a critical point, Hopf bifurcation occurs. To control the Hopf bifurcation, a time-delayed feedback controller using polynomial function is proposed to delay the onset of undesirable Hopf bifurcation. Numerical simulation results confirm that the new feedback controller using time delay is efficient in controlling Hopf bifurcation. This approach can be extended to study higher dimensional delay differential equations.<\/jats:p>","DOI":"10.1142\/s0218127405013587","type":"journal-article","created":{"date-parts":[[2005,9,29]],"date-time":"2005-09-29T09:34:54Z","timestamp":1127986494000},"page":"2643-2651","source":"Crossref","is-referenced-by-count":42,"title":["HOPF BIFURCATION CONTROL FOR AN INTERNET CONGESTION MODEL"],"prefix":"10.1142","volume":"15","author":[{"given":"Z.","family":"CHEN","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"YU","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(86)90095-2"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(98)80010-1"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(95)00827-6"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.56.R1334"},{"key":"rf6","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1142\/S0218127400000360","volume":"10","author":"Chen G. R.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2003.812809"},{"key":"rf8","volume-title":"Theory and Applications of Hopf Bifurcation","author":"Hassard B. D.","year":"1981"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1109\/90.974534"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1057\/palgrave.jors.2600523"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2000.0651"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(03)00269-8"},{"key":"rf13","first-page":"497","volume":"14","author":"Nayfeh A. H.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/17\/1\/006"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004905"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1515\/9783110879971"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.63.021902"},{"key":"rf18","unstructured":"P.\u00a0Yu, Bifurcation Control: Theory and Applications, eds. G. R.\u00a0Chen, D. J.\u00a0Hill and X.\u00a0Yu (Springer-Verlag, Berlin, 2003)\u00a0pp. 99\u2013126."},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404010291"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405013587","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T23:52:46Z","timestamp":1586476366000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405013587"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,8]]},"references-count":18,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,8]]}},"alternative-id":["10.1142\/S0218127405013587"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405013587","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,8]]}}}