{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T22:27:04Z","timestamp":1726439224231},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,2]]},"abstract":"<jats:p> We study the number of limit cycles of the discontinuous piecewise linear differential systems in \u211d<jats:sup>2n<\/jats:sup> with two zones separated by a hyperplane. Our main result shows that at most (8n - 6)<jats:sup>n-1<\/jats:sup> limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result, we use the averaging theory in a form where the differentiability of the system is not necessary. <\/jats:p>","DOI":"10.1142\/s0218127413500247","type":"journal-article","created":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T05:55:17Z","timestamp":1363758917000},"page":"1350024","source":"Crossref","is-referenced-by-count":3,"title":["ON THE NUMBER OF LIMIT CYCLES FOR DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS IN \u211d<sup>2n<\/sup> WITH TWO ZONES"],"prefix":"10.1142","volume":"23","author":[{"given":"JAUME","family":"LLIBRE","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FENG","family":"RONG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,3,20]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.3049"},{"key":"p_5","first-page":"51","volume":"20","author":"Broucke M.","year":"2001","journal-title":"Comput. Appl. Math."},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/j.bulsci.2003.09.002"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2011.08.006"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.08.013"},{"key":"p_10","first-page":"1101","volume":"7","author":"Coombes S.","year":"2008","journal-title":"SIAM J. Appl. Math."},{"key":"p_11","first-page":"45","volume":"141","author":"di Bernardo M.","year":"1998","journal-title":"IEEE Trans. Circuits Syst.-I.: Regul. Pap."},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127401002584"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498001728"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/14\/6\/311"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.10.002"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2012.32.2147"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.1997.3.235"},{"key":"p_20","first-page":"325","volume":"19","author":"Llibre J.","year":"2012","journal-title":"Discr. Impul. Syst. B"},{"journal-title":"Int. J. Bifurcation and Chaos, to appear.","year":"2011","author":"Llibre J.","key":"p_21"},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.1016\/0022-460X(83)90407-8"},{"key":"p_25","first-page":"207","volume":"95","author":"Sotomayor J.","year":"1996","journal-title":"Int. Conf. Differential Equations, Equadiff"},{"key":"p_26","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139901393500"},{"key":"p_27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.67.021908"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127413500247","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T08:05:02Z","timestamp":1565078702000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127413500247"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2]]},"references-count":19,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2013,3,20]]},"published-print":{"date-parts":[[2013,2]]}},"alternative-id":["10.1142\/S0218127413500247"],"URL":"https:\/\/doi.org\/10.1142\/s0218127413500247","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2013,2]]}}}