{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T16:54:29Z","timestamp":1780332869103,"version":"3.54.1"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,4]]},"abstract":"<jats:p> In this paper, we provide a lower bound for the maximum number of limit cycles of planar discontinuous piecewise linear differential systems defined in two half-planes separated by a straight line. Here, we only consider nonsliding limit cycles. For those systems, the interior of any limit cycle only contains a unique equilibrium point or a unique sliding segment. Moreover, the linear differential systems that we consider in every half-plane can have either a focus (F), or a node (N), or a saddle (S), these equilibrium points can be real or virtual. Then, we can consider six kinds of planar discontinuous piecewise linear differential systems: FF, FN, FS, NN, NS, SS. We provide for each of these types of discontinuous differential systems examples with two limit cycles. <\/jats:p>","DOI":"10.1142\/s0218127413500661","type":"journal-article","created":{"date-parts":[[2013,5,15]],"date-time":"2013-05-15T03:19:19Z","timestamp":1368587959000},"page":"1350066","source":"Crossref","is-referenced-by-count":41,"title":["LOWER BOUNDS FOR THE MAXIMUM NUMBER OF LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH A STRAIGHT LINE OF SEPARATION"],"prefix":"10.1142","volume":"23","author":[{"given":"J.","family":"LLIBRE","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques. Edifici C., 08193 Bellaterra, Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. A.","family":"TEIXEIRA","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade Estadual de Campinas, Caixa Postal 6065, 13083\u2013970, Campinas, SP, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"TORREGROSA","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques. Edifici C., 08193 Bellaterra, Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2013,5,14]]},"reference":[{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1137\/070707579"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02124750"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498001728"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/14\/6\/311"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.10.002"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2012.32.2147"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(02)00124-3"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412500575"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2012.03.022"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.1997.3.235"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-006-9057-7"},{"key":"p_18","first-page":"325","volume":"19","author":"Llibre J.","year":"2012","journal-title":"Dyn. Contin. Discr. Impuls. Syst. Ser. B"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2011.05.029"},{"key":"p_23","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139901393500"},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.67.021908"},{"key":"p_25","first-page":"690453","volume":"2012","author":"Xiong Y.","year":"2012","journal-title":"Abstr. Appl. Anal."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127413500661","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T02:00:59Z","timestamp":1565143259000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127413500661"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4]]},"references-count":16,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2013,5,14]]},"published-print":{"date-parts":[[2013,4]]}},"alternative-id":["10.1142\/S0218127413500661"],"URL":"https:\/\/doi.org\/10.1142\/s0218127413500661","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,4]]}}}