{"id":"https://openalex.org/W4386425859","doi":"https://doi.org/10.1142/s0218127423501237","title":"Crossing Limit Cycles Bifurcating from Two or Three Period Annuli in Discontinuous Planar Piecewise Linear Hamiltonian Differential Systems with Three Zones","display_name":"Crossing Limit Cycles Bifurcating from Two or Three Period Annuli in Discontinuous Planar Piecewise Linear Hamiltonian Differential Systems with Three Zones","publication_year":2023,"publication_date":"2023-08-01","ids":{"openalex":"https://openalex.org/W4386425859","doi":"https://doi.org/10.1142/s0218127423501237"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127423501237","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423501237","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://doi.org/10.1142/S0218127423501237","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028972310","display_name":"Denis de Carvalho Braga","orcid":"https://orcid.org/0000-0001-6265-6708"},"institutions":[{"id":"https://openalex.org/I8165072","display_name":"Universidade Federal de Itajub\u00e1","ror":"https://ror.org/00235nr42","country_code":"BR","type":"education","lineage":["https://openalex.org/I8165072"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Denis de Carvalho Braga","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Avenida BPS 1303, Pinheirinho, CEP: 37.500-903, Itajub\u00e1, MG, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Avenida BPS 1303, Pinheirinho, CEP: 37.500-903, Itajub\u00e1, MG, Brazil","institution_ids":["https://openalex.org/I8165072"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040520835","display_name":"Alexander Fernandes da Fonseca","orcid":"https://orcid.org/0000-0002-4145-8750"},"institutions":[{"id":"https://openalex.org/I8165072","display_name":"Universidade Federal de Itajub\u00e1","ror":"https://ror.org/00235nr42","country_code":"BR","type":"education","lineage":["https://openalex.org/I8165072"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Alexander Fernandes da Fonseca","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Avenida BPS 1303, Pinheirinho, CEP: 37.500-903, Itajub\u00e1, MG, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Avenida BPS 1303, Pinheirinho, CEP: 37.500-903, Itajub\u00e1, MG, Brazil","institution_ids":["https://openalex.org/I8165072"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003957478","display_name":"Luis Fernando Mello","orcid":"https://orcid.org/0000-0002-4989-3052"},"institutions":[{"id":"https://openalex.org/I8165072","display_name":"Universidade Federal de Itajub\u00e1","ror":"https://ror.org/00235nr42","country_code":"BR","type":"education","lineage":["https://openalex.org/I8165072"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Luis Fernando Mello","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Avenida BPS 1303, Pinheirinho, CEP: 37.500-903, Itajub\u00e1, MG, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Avenida BPS 1303, Pinheirinho, CEP: 37.500-903, Itajub\u00e1, MG, Brazil","institution_ids":["https://openalex.org/I8165072"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085486855","display_name":"Ronisio Moises Ribeiro","orcid":"https://orcid.org/0000-0001-8094-130X"},"institutions":[{"id":"https://openalex.org/I8165072","display_name":"Universidade Federal de Itajub\u00e1","ror":"https://ror.org/00235nr42","country_code":"BR","type":"education","lineage":["https://openalex.org/I8165072"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ronisio Moises Ribeiro","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Avenida BPS 1303, Pinheirinho, CEP: 37.500-903, Itajub\u00e1, MG, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Avenida BPS 1303, Pinheirinho, CEP: 37.500-903, Itajub\u00e1, MG, Brazil","institution_ids":["https://openalex.org/I8165072"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080134126","display_name":"Claudio Pessoa","orcid":"https://orcid.org/0000-0001-6790-1055"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Claudio Gomes Pessoa","raw_affiliation_strings":["Instituto de Bioci\u00eancias Letras e Ci\u00eancias Exatas, Universidade Estadual Paulista, Rua Cristov\u00e3o Colombo, 2265, CEP: 15.054-000, S.J. Rio Preto, SP, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Bioci\u00eancias Letras e Ci\u00eancias Exatas, Universidade Estadual Paulista, Rua Cristov\u00e3o Colombo, 2265, CEP: 15.054-000, S.J. Rio Preto, SP, Brazil","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5028972310"],"corresponding_institution_ids":["https://openalex.org/I8165072"],"apc_list":null,"apc_paid":null,"fwci":2.7963,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.90768541,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"33","issue":"10","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9585999846458435,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7600246667861938},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7004391551017761},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6792408227920532},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6004309058189392},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5765026211738586},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5679408311843872},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5639617443084717},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5266906023025513},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5217369794845581},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.08675941824913025}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7600246667861938},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7004391551017761},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6792408227920532},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6004309058189392},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5765026211738586},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5679408311843872},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5639617443084717},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5266906023025513},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5217369794845581},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.08675941824913025},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127423501237","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423501237","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:repositorio.unesp.br:11449/304219","is_oa":true,"landing_page_url":"http://doi.org/10.1142/S0218127423501237","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:UNESP","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:repositorio.unesp.br:11449/304219","is_oa":true,"landing_page_url":"http://doi.org/10.1142/S0218127423501237","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:UNESP","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4375231369","display_name":null,"funder_award_id":"APQ-01105-18","funder_id":"https://openalex.org/F4320322980","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais"},{"id":"https://openalex.org/G5645361881","display_name":null,"funder_award_id":"311921/2020-5","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G7467901041","display_name":null,"funder_award_id":"19/10269-3","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322980","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais","ror":"https://ror.org/00nc55f03"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1563280961","https://openalex.org/W1968107465","https://openalex.org/W2026267947","https://openalex.org/W2046380677","https://openalex.org/W2048408728","https://openalex.org/W2088972854","https://openalex.org/W2199630651","https://openalex.org/W2501875250","https://openalex.org/W2549538398","https://openalex.org/W2765944944","https://openalex.org/W2962808856","https://openalex.org/W3088944815","https://openalex.org/W3120702790","https://openalex.org/W3201642550","https://openalex.org/W4225576532"],"related_works":["https://openalex.org/W2765944944","https://openalex.org/W2137428669","https://openalex.org/W1631293748","https://openalex.org/W3088944815","https://openalex.org/W4327881149","https://openalex.org/W4251618568","https://openalex.org/W2039889532","https://openalex.org/W4313399542","https://openalex.org/W2184918219","https://openalex.org/W4280562183"],"abstract_inverted_index":{"The":[0],"main":[1],"topic":[2],"studied":[3,134],"in":[4,21,39,158,179],"this":[5,43],"article":[6],"is":[7,90,150,196],"the":[8,35,40,47,55,58,83,85,102,105,112,130,139,147,181,185,193],"number":[9,113,140,186],"of":[10,51,57,66,104,114,141,172,184,187],"crossing":[11,115,142],"limit":[12,116,143,188],"cycles":[13,117,144,189],"bifurcating":[14,145],"from":[15,92,121,146,192],"two":[16,76],"or":[17,153],"three":[18,30,72],"period":[19,122,148,194],"annuli":[20,123,149,195],"discontinuous":[22],"planar":[23],"piecewise":[24,68,131,174],"linear":[25,175],"Hamiltonian":[26,69,132],"differential":[27,177],"systems":[28,159],"with":[29,71],"zones.":[31],"With":[32],"regard":[33],"to":[34,110,155],"studies":[36],"already":[37,95,160],"published":[38],"literature":[41],"on":[42],"subject,":[44],"we":[45,167],"highlight":[46],"following":[48],"five":[49],"aspects":[50],"our":[52],"work:":[53],"(1)":[54],"expressions":[56,103],"first":[59],"order":[60],"Melnikov":[61,86,106],"functions":[62,87,107],"for":[63,98],"suitable":[64,125],"perturbations":[65],"a":[67,169,173],"system":[70,133,178],"zones":[73],"separated":[74],"by":[75],"parallel":[77],"lines":[78],"are":[79,88,108],"obtained":[80,89,157],"explicitly;":[81],"(2)":[82],"way":[84],"different":[91],"what":[93],"has":[94,136],"been":[96],"done":[97],"similar":[99,165],"studies;":[100],"(3)":[101],"used":[109],"estimate":[111],"that":[118,190],"bifurcate":[119,191],"simultaneously":[120],"under":[124],"polynomial":[126],"perturbations;":[127],"(4)":[128],"since":[129],"here":[135],"no":[137],"symmetry,":[138],"greater":[151],"than":[152],"equal":[154],"those":[156],"studied;":[161],"(5)":[162],"unlike":[163],"other":[164],"studies,":[166],"present":[168],"concrete":[170],"example":[171],"near-Hamiltonian":[176],"which":[180],"lower":[182],"bound":[183],"reached.":[197]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2025-12-25T23:11:45.687758","created_date":"2025-10-10T00:00:00"}