{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T00:50:52Z","timestamp":1776819052823,"version":"3.51.2"},"reference-count":14,"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":[[2012,8]]},"abstract":"<jats:p> As we know, Li\u00e9nard system is an important model of nonlinear oscillators, which has been widely studied. In this paper, we study the Hopf bifurcation of an analytic Li\u00e9nard system by perturbing a nilpotent center. We develop an efficient method to compute the coefficients b<jats:sub>l<\/jats:sub> appearing in the expansion of the first order Melnikov function by finding a set of equivalent quantities B<jats:sub>2l+1<\/jats:sub> which are able to calculate directly and can be used to study the number of small-amplitude limit cycles of the system. As an application, we investigate some polynomial Li\u00e9nard systems, obtaining a lower bound of the maximal number of limit cycles near a nilpotent center. <\/jats:p>","DOI":"10.1142\/s0218127412502033","type":"journal-article","created":{"date-parts":[[2012,9,17]],"date-time":"2012-09-17T04:52:34Z","timestamp":1347857554000},"page":"1250203","source":"Crossref","is-referenced-by-count":4,"title":["HOPF BIFURCATION OF LI\u00c9NARD SYSTEMS BY PERTURBING A NILPOTENT CENTER"],"prefix":"10.1142","volume":"22","author":[{"given":"JING","family":"SU","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JUNMIN","family":"YANG","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MAOAN","family":"HAN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,9,17]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01081886"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0147-9"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.02.010"},{"key":"rf4","first-page":"113","volume":"15","author":"Han M.","journal-title":"Ann. Diff. Eqns."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.6758"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408022226"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409025250"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.asr.2008.08.025"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.bulsci.2006.11.006"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409023949"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.10.051"},{"key":"rf12","first-page":"441","volume":"16","author":"Li C.","journal-title":"Extracta Mathematicae"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403006352"},{"key":"rf14","first-page":"161","volume":"8","author":"Llibre J.","journal-title":"Dyn. Contin. Discr. Impuls. Syst. Series A: Math. Anal."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127412502033","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T15:51:03Z","timestamp":1565106663000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127412502033"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8]]},"references-count":14,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2012,9,17]]},"published-print":{"date-parts":[[2012,8]]}},"alternative-id":["10.1142\/S0218127412502033"],"URL":"https:\/\/doi.org\/10.1142\/s0218127412502033","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8]]}}}