{"id":"https://openalex.org/W2008867377","doi":"https://doi.org/10.1080/00207160.2015.1046847","title":"Sufficient conditions for the existence of periodic solutions of the extended Duffing\u2013Van der Pol oscillator","display_name":"Sufficient conditions for the existence of periodic solutions of the extended Duffing\u2013Van der Pol oscillator","publication_year":2015,"publication_date":"2015-04-30","ids":{"openalex":"https://openalex.org/W2008867377","doi":"https://doi.org/10.1080/00207160.2015.1046847","mag":"2008867377"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1046847","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1046847","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1404.0608","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009216020","display_name":"Rodrigo D. Euz\u00e9bio","orcid":"https://orcid.org/0000-0001-8083-5216"},"institutions":[{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]},{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]},{"id":"https://openalex.org/I4210122226","display_name":"Centre de Recerca Matem\u00e0tica","ror":"https://ror.org/020s51w82","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210122226","https://openalex.org/I4387153040"]}],"countries":["BR","ES"],"is_corresponding":false,"raw_author_name":"Rodrigo D. Euz\u00e9bio","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain; Departament de Matem\u00e1tica, IBILCE, UNESP, Rua Cristovao Colombo 2265, Jardim Nazareth, CEP 15.054\u201300, Sao Jos\u00e9 de Rio Preto, SP, Brazil","Departament de Matem\u00e1tica, IBILCE, UNESP, Rua Cristovao Colombo 2265, Jardim Nazareth, CEP 15.054\u201300, Sao Jos\u00e9 de Rio Preto, SP, Brazil","Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain; Departament de Matem\u00e1tica, IBILCE, UNESP, Rua Cristovao Colombo 2265, Jardim Nazareth, CEP 15.054\u201300, Sao Jos\u00e9 de Rio Preto, SP, Brazil","institution_ids":["https://openalex.org/I4210122226","https://openalex.org/I123044942"]},{"raw_affiliation_string":"Departament de Matem\u00e1tica, IBILCE, UNESP, Rua Cristovao Colombo 2265, Jardim Nazareth, CEP 15.054\u201300, Sao Jos\u00e9 de Rio Preto, SP, Brazil","institution_ids":["https://openalex.org/I879563668"]},{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046015548","display_name":"Jaume Llibre","orcid":"https://orcid.org/0000-0002-9511-5999"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jaume Llibre","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046015548"],"corresponding_institution_ids":["https://openalex.org/I123044942"],"apc_list":null,"apc_paid":null,"fwci":0.5408,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.66146822,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"93","issue":"8","first_page":"1358","last_page":"1382"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10244","display_name":"Chaos control and synchronization","score":0.9955000281333923,"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/van-der-pol-oscillator","display_name":"Van der Pol oscillator","score":0.9446017742156982},{"id":"https://openalex.org/keywords/duffing-equation","display_name":"Duffing equation","score":0.7345669269561768},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5737192034721375},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5645700097084045},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5157187581062317},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4223264157772064},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.41444331407546997},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40475741028785706},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2493779957294464},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16615772247314453},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1203601062297821},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11209458112716675},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.055643707513809204}],"concepts":[{"id":"https://openalex.org/C98010927","wikidata":"https://www.wikidata.org/wiki/Q2081515","display_name":"Van der Pol oscillator","level":3,"score":0.9446017742156982},{"id":"https://openalex.org/C132323500","wikidata":"https://www.wikidata.org/wiki/Q675387","display_name":"Duffing equation","level":3,"score":0.7345669269561768},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5737192034721375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5645700097084045},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5157187581062317},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4223264157772064},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.41444331407546997},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40475741028785706},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2493779957294464},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16615772247314453},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1203601062297821},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11209458112716675},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.055643707513809204},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1080/00207160.2015.1046847","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1046847","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1404.0608","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.0608","pdf_url":"https://arxiv.org/pdf/1404.0608","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:ddd.uab.cat:221043","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/221043","pdf_url":"https://ddd.uab.cat/record/221043","source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"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":null,"raw_type":"Article"},{"id":"pmh:oai:americanae.aecid.es:1752892","is_oa":true,"landing_page_url":"http://hdl.handle.net/11449/171875","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"reponame:Reposit\u00f3rio Institucional da UNESP","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:dnet:uabarcelona_::e424aa1057d68b221a8a5672c7ad1718","is_oa":false,"landing_page_url":"http://ddd.uab.cat/record/221043","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repositorio.unesp.br:11449/171875","is_oa":true,"landing_page_url":"http://doi.org/10.1080/00207160.2015.1046847","pdf_url":null,"source":{"id":"https://openalex.org/S4377196277","display_name":"UNESP Institutional Repository (S\u00e3o Paulo State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I879563668","host_organization_name":"Universidade Estadual Paulista (Unesp)","host_organization_lineage":["https://openalex.org/I879563668"],"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:arXiv.org:1404.0608","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.0608","pdf_url":"https://arxiv.org/pdf/1404.0608","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.5299999713897705,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G2847775500","display_name":null,"funder_award_id":"2014SGR568","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G3676677543","display_name":null,"funder_award_id":"88881.030454/2013-01","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"}],"funders":[{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320334830","display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca","ror":"https://ror.org/01n4pqe45"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W571526444","https://openalex.org/W602770468","https://openalex.org/W639974373","https://openalex.org/W1561016548","https://openalex.org/W1977063515","https://openalex.org/W1977100588","https://openalex.org/W1983924943","https://openalex.org/W1988707330","https://openalex.org/W2007285678","https://openalex.org/W2008423115","https://openalex.org/W2009659872","https://openalex.org/W2019058308","https://openalex.org/W2028092681","https://openalex.org/W2029309995","https://openalex.org/W2029777464","https://openalex.org/W2029798704","https://openalex.org/W2045746056","https://openalex.org/W2053700530","https://openalex.org/W2057488602","https://openalex.org/W2077430696","https://openalex.org/W2079956827","https://openalex.org/W2082503639","https://openalex.org/W2090715225","https://openalex.org/W2091253744","https://openalex.org/W2091657382","https://openalex.org/W2101714536","https://openalex.org/W2146364181","https://openalex.org/W2158334808","https://openalex.org/W2226136747","https://openalex.org/W4237780066"],"related_works":["https://openalex.org/W1969774171","https://openalex.org/W4281721123","https://openalex.org/W2335513744","https://openalex.org/W2967847967","https://openalex.org/W1602795945","https://openalex.org/W1977392020","https://openalex.org/W2886649776","https://openalex.org/W4294368465","https://openalex.org/W2031702848","https://openalex.org/W2049992072"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"some":[3,80,97],"aspects":[4],"on":[5],"the":[6,10,22,27,31,57,77,88,93],"periodic":[7,46,54,81],"solutions":[8,47,55],"of":[9,21,26,56,79],"extended":[11,32],"Duffing\u2013Van":[12,33],"der":[13,34],"Pol":[14,35],"oscillator":[15],"are":[16,71,90],"discussed.":[17],"Doing":[18],"different":[19],"rescaling":[20,62],"variables":[23],"and":[24,87,96],"parameters":[25],"system":[28],"associated":[29],"with":[30],"oscillator,":[36],"we":[37,63,75],"show":[38],"that":[39,74],"it":[40],"can":[41],"bifurcate":[42],"one":[43],"or":[44],"three":[45],"from":[48],"a":[49],"two-dimensional":[50],"manifold":[51],"filled":[52],"by":[53],"referred":[58],"system.":[59],"For":[60],"each":[61],"exhibit":[64],"concrete":[65],"values":[66],"for":[67],"which":[68],"these":[69],"bounds":[70],"reached.":[72],"Beyond":[73],"characterize":[76],"stability":[78],"solutions.":[82],"Our":[83],"approach":[84],"is":[85],"analytical":[86],"results":[89],"obtained":[91],"using":[92],"averaging":[94],"theory":[95],"algebraic":[98],"techniques.":[99]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
