{"id":"https://openalex.org/W2032926717","doi":"https://doi.org/10.1142/s0218127414500564","title":"More Than Three Limit Cycles in Discontinuous Piecewise Linear Differential Systems with Two Zones in the Plane","display_name":"More Than Three Limit Cycles in Discontinuous Piecewise Linear Differential Systems with Two Zones in the Plane","publication_year":2014,"publication_date":"2014-04-01","ids":{"openalex":"https://openalex.org/W2032926717","doi":"https://doi.org/10.1142/s0218127414500564","mag":"2032926717"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127414500564","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500564","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"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":["Campus Avan\u00e7ado de Itabira, Universidade Federal de Itajub\u00e1, Rua S\u00e3o Paulo 377, Bairro Amazonas, CEP 35.900\u2013373, Itabira, MG, Brazil"],"affiliations":[{"raw_affiliation_string":"Campus Avan\u00e7ado de Itabira, Universidade Federal de Itajub\u00e1, Rua S\u00e3o Paulo 377, Bairro Amazonas, CEP 35.900\u2013373, Itabira, MG, Brazil","institution_ids":["https://openalex.org/I8165072"]}]},{"author_position":"last","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\u2013903, 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\u2013903, Itajub\u00e1, MG, Brazil","institution_ids":["https://openalex.org/I8165072"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028972310"],"corresponding_institution_ids":["https://openalex.org/I8165072"],"apc_list":null,"apc_paid":null,"fwci":4.679,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.94703699,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"24","issue":"04","first_page":"1450056","last_page":"1450056"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7774540185928345},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.7617402076721191},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.7181963920593262},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6581527590751648},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6428632736206055},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5601941347122192},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5482292175292969},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5357673764228821},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5073608756065369},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.4169090986251831},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2209455966949463},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20558154582977295},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10626804828643799}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7774540185928345},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.7617402076721191},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7181963920593262},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6581527590751648},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6428632736206055},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5601941347122192},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5482292175292969},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5357673764228821},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5073608756065369},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.4169090986251831},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2209455966949463},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20558154582977295},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10626804828643799},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127414500564","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500564","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1980228211","https://openalex.org/W2016789606","https://openalex.org/W2039889532","https://openalex.org/W2054652000","https://openalex.org/W2075523193","https://openalex.org/W2092046534","https://openalex.org/W2500278320","https://openalex.org/W4302769929"],"related_works":["https://openalex.org/W2765944944","https://openalex.org/W4226164715","https://openalex.org/W3096660584","https://openalex.org/W1596838019","https://openalex.org/W3182827720","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3208509670","https://openalex.org/W2100864966","https://openalex.org/W2109304297"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,23,49],"study":[4],"the":[5,19,25,36,51,62],"existence":[6,26,52],"of":[7,27,53],"limit":[8,44,67],"cycles":[9,68],"for":[10,69],"piecewise":[11,28,54],"linear":[12,29,55],"differential":[13,30,56],"systems":[14,31,57],"with":[15,32,38,58],"two":[16,33,59],"zones":[17,34,60],"in":[18,35,61],"plane.":[20],"More":[21],"precisely,":[22],"prove":[24],"plane":[37,63],"four,":[39],"five,":[40],"six":[41],"and":[42],"seven":[43],"cycles.":[45],"From":[46],"our":[47],"results":[48],"conjecture":[50],"having":[64],"exactly":[65],"n":[66,71],"all":[70],"\u2208":[72],"\u2115.":[73]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2025-10-10T00:00:00"}