{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,12]],"date-time":"2025-08-12T22:22:54Z","timestamp":1755037374510},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,5]]},"abstract":"<jats:p>This paper presents a study on the problem of Hopf bifurcation control of time delayed systems with weak nonlinearity via delayed feedback control. It focusses on two control objectives: one is to annihilate the periodic solution, namely to perform a linear delayed feedback control so that the trivial equilibrium is asymptotically stable, and the other is to obtain an asymptotically stable periodic solution with given amplitude via linear or nonlinear delayed feedback control. On the basis of the averaging method and the center manifold reduction for delayed differential equations, an effective method is developed for this problem. It has been shown that a linear delayed feedback can always stabilize the unstable trivial equilibrium of the system, and a linear or nonlinear delayed feedback control can always achieve an asymptotically stable periodic solution with desired amplitude. The illustrative example shows that the theoretical prediction is in very good agreement with the simulation results, and that the method is valid with high accuracy not only for delayed systems with weak nonlinearity and via weak feedback control, but also for those when the nonlinearity and feedback control are not small.<\/jats:p>","DOI":"10.1142\/s0218127405012909","type":"journal-article","created":{"date-parts":[[2005,7,7]],"date-time":"2005-07-07T13:48:02Z","timestamp":1120744082000},"page":"1787-1799","source":"Crossref","is-referenced-by-count":4,"title":["HOPF BIFURCATION CONTROL OF DELAYED SYSTEMS WITH WEAK NONLINEARITY VIA DELAYED STATE FEEDBACK"],"prefix":"10.1142","volume":"15","author":[{"given":"ZAIHUA","family":"WANG","sequence":"first","affiliation":[{"name":"Institute of Vibration Engineering Research, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"HAIYAN","family":"HU","sequence":"additional","affiliation":[{"name":"Institute of Vibration Engineering Research, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, P. R. China"}],"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\/0022-0396(83)90037-2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1080\/00207170110107265"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498000504"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1063\/1.166395"},{"key":"rf6","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1142\/S0218127400000360","volume":"10","author":"Chen G.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1995.1144"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(66)90063-5"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/b100032"},{"key":"rf10","volume-title":"Theory and Applications of Hopf Bifurcation","author":"Hassard B. D.","year":"1981"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2003.07.006"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0997-3"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/S0093-6413(03)00006-5"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.78.203"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1998.3523"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1142\/3070"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/18.1.15"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1115\/1.2831178"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(95)00654-L"},{"key":"rf20","volume-title":"Stability of Dynamical Systems with Time Delays","author":"Qin Y. X.","year":"1989"},{"key":"rf21","first-page":"525","volume":"72","author":"Stech H. W.","journal-title":"J. Math. Anal. Appl."},{"key":"rf22","first-page":"795","volume":"279","author":"Wang Z. H.","journal-title":"J. Sound Vibr."},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(03)00049-6"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405012909","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T05:12:32Z","timestamp":1586322752000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405012909"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,5]]},"references-count":23,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,5]]}},"alternative-id":["10.1142\/S0218127405012909"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405012909","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,5]]}}}