{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T12:13:27Z","timestamp":1781266407639,"version":"3.54.1"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["19\/10269-3"],"award-info":[{"award-number":["19\/10269-3"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["18\/19726-5"],"award-info":[{"award-number":["18\/19726-5"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["88882.434343\/2019-01"],"award-info":[{"award-number":["88882.434343\/2019-01"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,6,30]]},"abstract":"<jats:p> In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in a discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines. We prove that if the central subsystem, i.e. the system defined between the two parallel lines, has a real center and the other subsystems have centers or saddles, then we have at least three limit cycles that appear after perturbations of the periodic annulus. For this, we study the number of zeros of a Melnikov function for piecewise Hamiltonian system and present a normal form for this system in order to simplify the computations. <\/jats:p>","DOI":"10.1142\/s0218127422501140","type":"journal-article","created":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T08:43:59Z","timestamp":1656578639000},"source":"Crossref","is-referenced-by-count":8,"title":["Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones"],"prefix":"10.1142","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6790-1055","authenticated-orcid":false,"given":"Claudio","family":"Pessoa","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, IBILCE\u2013UNESP, R. Cristov\u00e3o Colombo, 2265, CEP 15.054-000, S. J. Rio Preto, SP, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ronisio","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, IBILCE\u2013UNESP, R. Cristov\u00e3o Colombo, 2265, CEP 15.054-000, S. J. Rio Preto, SP, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2022,6,30]]},"reference":[{"key":"S0218127422501140BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/B978-1-4831-6724-4.50014-9"},{"key":"S0218127422501140BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-013-0862-3"},{"key":"S0218127422501140BIB003","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2013.33.3915"},{"key":"S0218127422501140BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/31.55064"},{"key":"S0218127422501140BIB005","volume-title":"Piecewise-Smooth Dynamical Systems: Theory and Applications","author":"di Bernardo M.","year":"2008"},{"key":"S0218127422501140BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-017-0844-2"},{"key":"S0218127422501140BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(61)86902-6"},{"key":"S0218127422501140BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127420501576"},{"key":"S0218127422501140BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498001728"},{"key":"S0218127422501140BIB010","doi-asserted-by":"publisher","DOI":"10.1137\/11083928X"},{"key":"S0218127422501140BIB011","doi-asserted-by":"publisher","DOI":"10.5565\/PUBLMAT_Extra14_13"},{"key":"S0218127422501140BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2013.05.012"},{"key":"S0218127422501140BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2018.12.024"},{"key":"S0218127422501140BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s12346-021-00496-4"},{"key":"S0218127422501140BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127417500225"},{"key":"S0218127422501140BIB016","first-page":"1","volume":"5","author":"Liu X.","year":"2010","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"S0218127422501140BIB017","first-page":"203","volume":"18","author":"Llibre J.","year":"2011","journal-title":"Dyn. Contin. Discr. Impul. Syst.: Ser. A"},{"key":"S0218127422501140BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0657-2"},{"key":"S0218127422501140BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-013-0393-2"},{"key":"S0218127422501140BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-015-9244-y"},{"key":"S0218127422501140BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3866-6"},{"key":"S0218127422501140BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2018.07.024"},{"key":"S0218127422501140BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(70)90023-X"},{"key":"S0218127422501140BIB024","doi-asserted-by":"publisher","DOI":"10.1109\/JRPROC.1962.288235"},{"key":"S0218127422501140BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2015.11.041"},{"key":"S0218127422501140BIB026","volume-title":"Mathematica","author":"Wolfram Research, Inc.","year":"2020"},{"key":"S0218127422501140BIB027","first-page":"361","volume":"10","author":"Xiong Y.","year":"2020","journal-title":"J. Appl. Anal. Comput."},{"key":"S0218127422501140BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2021.103333"},{"key":"S0218127422501140BIB029","first-page":"2362","volume":"6","author":"Yang J.","year":"2020","journal-title":"J. Appl. Anal. Comput."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127422501140","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T08:46:19Z","timestamp":1656578779000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218127422501140"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,30]]},"references-count":29,"journal-issue":{"issue":"08","published-print":{"date-parts":[[2022,6,30]]}},"alternative-id":["10.1142\/S0218127422501140"],"URL":"https:\/\/doi.org\/10.1142\/s0218127422501140","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,30]]},"article-number":"2250114"}}