{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:07:58Z","timestamp":1772291278989,"version":"3.50.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2015,10]]},"abstract":"<jats:p> We study a class of discontinuous piecewise linear differential systems with two zones separated by the straight line x = 0. In x &gt; 0, we have a linear saddle with its equilibrium point living in x &gt; 0, and in x &lt; 0 we have a linear differential center. Let p be the equilibrium point of this linear center, when p lives in x &lt; 0, we say that it is real, and when p lives in x &gt; 0 we say that it is virtual. We assume that this discontinuous piecewise linear differential system formed by the center and the saddle has a center q surrounded by periodic orbits ending in a homoclinic orbit of the saddle, independent if p is real, virtual or p is in x = 0. Note that q = p if p is real or p is in x = 0. We perturb these three classes of systems, according to the position of p, inside the class of all discontinuous piecewise linear differential systems with two zones separated by x = 0. Let N be the maximum number of limit cycles which can bifurcate from the periodic solutions of the center q with these perturbations. Our main results show that N = 2 when p is on x = 0, and N \u2265 2 when p is a real or virtual center. Furthermore, when p is a real center we found an example satisfying N \u2265 3. <\/jats:p>","DOI":"10.1142\/s0218127415501448","type":"journal-article","created":{"date-parts":[[2015,10,27]],"date-time":"2015-10-27T06:59:44Z","timestamp":1445929184000},"page":"1550144","source":"Crossref","is-referenced-by-count":52,"title":["Limit Cycles Bifurcating from the Periodic Orbits of a Discontinuous Piecewise Linear Differentiable Center with Two Zones"],"prefix":"10.1142","volume":"25","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":"Douglas D.","family":"Novaes","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade Estadual de Campinas, Rua S\u00e9rgio Baruque de Holanda, 651, Cidade Universit\u00e1ria Zeferino Vaz, CEP 13083-859, Campinas, S\u00e3o Paulo, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco A.","family":"Teixeira","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade Estadual de Campinas, Rua S\u00e9rgio Baruque de Holanda, 651, Cidade Universit\u00e1ria Zeferino Vaz, CEP 13083-859, Campinas, S\u00e3o Paulo, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,10,26]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/B978-1-4831-6724-4.50014-9"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2013.02.007"},{"key":"rf3","volume-title":"Computing Methods, Volume II","author":"Berezin I. 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