{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:46Z","timestamp":1740134566553,"version":"3.37.3"},"reference-count":24,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51277128","51377117"],"award-info":[{"award-number":["51277128","51377117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51277128","51377117"],"award-info":[{"award-number":["51277128","51377117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>One type of bifurcation named oscillation emergence bifurcation (OEB) found in time-delayed linear time invariant (abbr. LTI) systems is fully studied. The definition of OEB is initially put forward according to the eigenvalue variation. It is revealed that a real eigenvalue splits into a pair of conjugated complex eigenvalues when an OEB occurs, which means the number of the system eigenvalues will increase by one and a new oscillation mode will emerge. Next, a method to determine OEB bifurcation in the time-delayed LTI system with single lag is developed based on Lambert W function. A one-dimensional (1-dim) time-delayed system is firstly employed to explain the mechanism of OEB bifurcation. Then, methods to determine the OEB bifurcation in 1-dim, 2-dim, and high-dimension time-delayed LTI systems are derived. Finally, simulation results validate the correctness and effectiveness of the presented method. Since OEB bifurcation occurs with a new oscillation mode emerging, work of this paper is useful to explore the complex phenomena and the stability of time-delayed dynamic systems.<\/jats:p>","DOI":"10.1155\/2014\/823937","type":"journal-article","created":{"date-parts":[[2014,7,3]],"date-time":"2014-07-03T17:09:26Z","timestamp":1404407366000},"page":"1-12","source":"Crossref","is-referenced-by-count":0,"title":["A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag"],"prefix":"10.1155","volume":"2014","author":[{"given":"Yu","family":"Xiaodan","sequence":"first","affiliation":[{"name":"Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, China"}]},{"given":"Jia","family":"Hongjie","sequence":"additional","affiliation":[{"name":"Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, China"}]},{"given":"Wang","family":"Chengshan","sequence":"additional","affiliation":[{"name":"Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, China"}]},{"given":"Jiang","family":"Yilang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, China"}]}],"member":"311","reference":[{"year":"2003","key":"1"},{"year":"1997","key":"2"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2013.08.011"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.memsci.2013.08.001"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2013.08.010"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.ces.2012.08.045"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2013.07.025"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2007.06.020"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1007\/s11431-013-5165-x"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2006.876385"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/s11431-014-5569-2"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2013.2255951"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2002.1000275"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2011.2161028"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413500144"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-006-9117-x"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2011.2173385"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2010.2045437"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/260798"},{"issue":"24","key":"23","first-page":"10","volume":"36","year":"2012","journal-title":"Automation of Electric Power Systems"},{"issue":"1","key":"24","first-page":"1","volume":"21","year":"1996","journal-title":"The Mathematical Scientist"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/BF02124750"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2007.04.001"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2005.05.020"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/823937.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/823937.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/823937.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,29]],"date-time":"2016-07-29T05:23:36Z","timestamp":1469769816000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/823937\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":24,"alternative-id":["823937","823937"],"URL":"https:\/\/doi.org\/10.1155\/2014\/823937","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}