{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T15:08:40Z","timestamp":1778684920022,"version":"3.51.4"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>In this paper, we consider local critical periods of planar vector field. Particular attention is given to revertible systems with polynomial functions up to third degree. It is assumed that the origin of the system is a center. Symbolic and numerical computations are employed to show that the general cubic revertible systems can have six local critical periods, which is the maximal number of local critical periods that cubic revertible systems may have. This new result corrects that in the literature: general cubic revertible systems can at most have four local critical periods.<\/jats:p>","DOI":"10.1142\/s0218127409022981","type":"journal-article","created":{"date-parts":[[2009,3,20]],"date-time":"2009-03-20T10:36:08Z","timestamp":1237545368000},"page":"419-433","source":"Crossref","is-referenced-by-count":19,"title":["CRITICAL PERIODS OF PLANAR REVERTIBLE VECTOR FIELD WITH THIRD-DEGREE POLYNOMIAL FUNCTIONS"],"prefix":"10.1142","volume":"19","author":[{"given":"PEI","family":"YU","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada"},{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MAOAN","family":"HAN","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"181","volume":"30","author":"Bautin N.","journal-title":"Mat. Sb. (N.S.)"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1989-0930075-2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8159-4"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511665639"},{"key":"rf5","volume-title":"Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields","author":"Guckenheimer J.","year":"1993"},{"key":"rf6","volume-title":"Periodic Solution and Bifurcation Theory of Dynamical Systems","author":"Han M.","year":"2002"},{"key":"rf7","doi-asserted-by":"crossref","first-page":"67","DOI":"10.3934\/mbe.2006.3.67","volume":"3","author":"Han M.","journal-title":"Math. Biosci. Engin."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1902-00923-3"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403006352"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406015155"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6374-6"},{"key":"rf12","volume-title":"Methods of Normal Forms","author":"Nayfeh A. H.","year":"1993"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1993-063-7"},{"key":"rf14","series-title":"Transl. Math. Monographs","volume-title":"Theory of Limit Cycles","volume":"66","author":"Ye Y. Q.","year":"1986"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1997.1347"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.3934\/cpaa.2004.3.515"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405013289"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(04)00599-5"},{"key":"rf19","first-page":"151","volume":"49","author":"Yu P.","journal-title":"The Fields Instit. Commun."},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(00)00195-4"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409022981","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T00:18:48Z","timestamp":1589674728000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409022981"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":20,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1142\/S0218127409022981"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409022981","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}