{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T13:50:33Z","timestamp":1781013033857,"version":"3.54.1"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,3]]},"abstract":"<jats:p> In this paper, we mainly discuss Hopf bifurcation for planar nonsmooth general systems and Li\u00e9nard systems with foci of parabolic\u2013parabolic (PP) or focus\u2013parabolic (FP) type. For the bifurcation near a focus, when the focus is kept fixed under perturbations we prove that there are at most k limit cycles which can be produced from an elementary weak focus of order 2k + 2 ( resp. k + 1)(k \u2265 1) if the focus is of PP (resp. FP) type, and we present the conditions to ensure these upper bounds are achievable. For the bifurcation near a center, the Hopf cyclicicy is studied for these systems. Some interesting applications are presented. <\/jats:p>","DOI":"10.1142\/s0218127412500575","type":"journal-article","created":{"date-parts":[[2012,2,16]],"date-time":"2012-02-16T01:41:54Z","timestamp":1329356514000},"page":"1250057","source":"Crossref","is-referenced-by-count":17,"title":["DEGENERATE HOPF BIFURCATION IN NONSMOOTH PLANAR SYSTEMS"],"prefix":"10.1142","volume":"22","author":[{"given":"FENG","family":"LIANG","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"},{"name":"Department of Mathematics, Anhui Normal University, Wuhu 241000, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MAOAN","family":"HAN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7188"},{"key":"rf2","volume-title":"Piecewise-Smooth Dynamical Systems Theory and Applications","author":"di Bernardo M.","year":"2008"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2007.09.045"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7793-9"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403007618"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.6758"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.10.002"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0103843"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409024177"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2010.06.012"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-005-0606-8"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127412500575","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:36:07Z","timestamp":1565127367000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127412500575"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3]]},"references-count":11,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,5,2]]},"published-print":{"date-parts":[[2012,3]]}},"alternative-id":["10.1142\/S0218127412500575"],"URL":"https:\/\/doi.org\/10.1142\/s0218127412500575","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3]]}}}