{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T08:32:18Z","timestamp":1758702738007},"reference-count":13,"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":[[2005,8]]},"abstract":"<jats:p> We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of piecewise linear differential systems, which appears in a natural way in control theory. Our main result shows that three is an upper bound for the number of limit cycles, up to first-order expansion of the displacement function with respect to the small parameter. Moreover, this upper bound is reached. For proving this result we use the averaging method in a form where the differentiability of the system is not needed. <\/jats:p>","DOI":"10.1142\/s0218127405013599","type":"journal-article","created":{"date-parts":[[2005,9,29]],"date-time":"2005-09-29T09:34:54Z","timestamp":1127986494000},"page":"2653-2662","source":"Crossref","is-referenced-by-count":12,"title":["BIFURCATION OF LIMIT CYCLES FROM A FOUR-DIMENSIONAL CENTER IN CONTROL SYSTEMS"],"prefix":"10.1142","volume":"15","author":[{"given":"ADRIANA","family":"BUIC\u0102","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Babe\u015f-Bolyai University of Cluj-Napoca, Romania"}]},{"given":"JAUME","family":"LLIBRE","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08913 Bellaterra, Barcelona, Spain"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.bulsci.2003.09.002"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2002.1001950"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8159-4"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499000638"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"rf6","first-page":"1","volume":"21","author":"Han M.","journal-title":"Acta Math. Appl. Sin."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(97)00669-X"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1080\/02681119608806216"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(95)00129-J"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403007047"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(03)00122-6"},{"key":"rf12","volume-title":"Degree Theory","author":"Lloyd N. G.","year":"1978"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61453-8"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405013599","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:04:26Z","timestamp":1565190266000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405013599"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,8]]},"references-count":13,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,8]]}},"alternative-id":["10.1142\/S0218127405013599"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405013599","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,8]]}}}