{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T16:48:42Z","timestamp":1777913322856,"version":"3.51.4"},"reference-count":19,"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":[[2004,8]]},"abstract":"<jats:p> The Hopf bifurcation, saddle connection loop bifurcation and Poincar\u00e9 bifurcation of the generalized Rayleigh\u2013Li\u00e9nard oscillator \u1e8c+aX+2bX<jats:sup>3<\/jats:sup>+\u03b5(c<jats:sub>3<\/jats:sub>+c<jats:sub>2<\/jats:sub>X<jats:sup>2<\/jats:sup>+c<jats:sub>1<\/jats:sub>X<jats:sup>4<\/jats:sup>+c<jats:sub>4<\/jats:sub>\u1e8a<jats:sup>2<\/jats:sup>)\u1e8a=0 are studied. It is proved that for the case a&lt;0, b&gt;0 the system has at most six limit cycles bifurcated from Hopf bifurcation or has at least seven limit cycles bifurcated from the double homoclinic loop. For the case a&gt;0, b&lt;0 the system has at most three limit cycles bifurcated from Hopf bifurcation or has three limit cycles bifurcated from the heteroclinic loop. <\/jats:p>","DOI":"10.1142\/s0218127404011132","type":"journal-article","created":{"date-parts":[[2004,9,17]],"date-time":"2004-09-17T10:44:54Z","timestamp":1095417894000},"page":"2905-2914","source":"Crossref","is-referenced-by-count":25,"title":["ON THE STUDY OF LIMIT CYCLES OF THE GENERALIZED RAYLEIGH\u2013LIENARD OSCILLATOR"],"prefix":"10.1142","volume":"14","author":[{"given":"YUHAI","family":"WU","sequence":"first","affiliation":[{"name":"Institute of Mathematics Zhejiang University of Sciences, Hangzhou, 310018, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MAOAN","family":"HAN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"XIANFENG","family":"CHEN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"190","volume":"211","author":"Armengonl G.","journal-title":"J. Math. Anal. Appl."},{"key":"rf2","first-page":"181","volume":"30","author":"Bautin N. N.","journal-title":"Mat. Sbornik (N. S.)"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1998.1997"},{"key":"rf4","first-page":"579","volume":"102","author":"Burnette J.","journal-title":"J. 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