{"id":"https://openalex.org/W3017264843","doi":"https://doi.org/10.1142/s0218127420500510","title":"Limit Cycles Bifurcating from a Family of Reversible Quadratic Centers via Averaging Theory","display_name":"Limit Cycles Bifurcating from a Family of Reversible Quadratic Centers via Averaging Theory","publication_year":2020,"publication_date":"2020-03-30","ids":{"openalex":"https://openalex.org/W3017264843","doi":"https://doi.org/10.1142/s0218127420500510","mag":"3017264843"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420500510","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420500510","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":"https://ddd.uab.cat/record/228110","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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, Bellaterra, Barcelona 08193, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9511-5999","affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Bellaterra, Barcelona 08193, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039381136","display_name":"Arefeh Nabavi","orcid":null},"institutions":[{"id":"https://openalex.org/I170013655","display_name":"Isfahan University of Technology","ror":"https://ror.org/00af3sa43","country_code":"IR","type":"education","lineage":["https://openalex.org/I170013655"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Arefeh Nabavi","raw_affiliation_strings":["Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran","institution_ids":["https://openalex.org/I170013655"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051472374","display_name":"Marzieh Mousavi","orcid":null},"institutions":[{"id":"https://openalex.org/I170013655","display_name":"Isfahan University of Technology","ror":"https://ror.org/00af3sa43","country_code":"IR","type":"education","lineage":["https://openalex.org/I170013655"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Marzieh Mousavi","raw_affiliation_strings":["Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran","institution_ids":["https://openalex.org/I170013655"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5046015548"],"corresponding_institution_ids":["https://openalex.org/I123044942"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1261708,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"04","first_page":"2050051","last_page":"2050051"},"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":1.0,"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":1.0,"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":0.9664999842643738,"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":0.6664032936096191},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6624205708503723},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6613470315933228},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.6369730234146118},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5224006175994873},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5106728672981262},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.49085599184036255},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4726085960865021},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44569116830825806},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.4221354126930237},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39104050397872925},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.345918744802475},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12213465571403503},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08582928776741028}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6664032936096191},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6624205708503723},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6613470315933228},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.6369730234146118},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5224006175994873},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5106728672981262},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.49085599184036255},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4726085960865021},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44569116830825806},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.4221354126930237},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39104050397872925},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.345918744802475},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12213465571403503},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08582928776741028},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218127420500510","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420500510","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:ddd.uab.cat:228110","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/228110","pdf_url":"https://ddd.uab.cat/record/228110","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:dnet:uabarcelona_::d91b067ed0fbb38dc55cd186d644c23c","is_oa":false,"landing_page_url":"http://ddd.uab.cat/record/228110","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"}],"best_oa_location":{"id":"pmh:oai:ddd.uab.cat:228110","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/228110","pdf_url":"https://ddd.uab.cat/record/228110","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1423109669","display_name":null,"funder_award_id":"MSCA-RISE-2017-777911","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G1545329600","display_name":null,"funder_award_id":"MTM2016-77278-P","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2133003115","display_name":null,"funder_award_id":"MSCA-RISE-2017-777911","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G2436355136","display_name":null,"funder_award_id":"MSCA-RISE-2017","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G3345895242","display_name":null,"funder_award_id":"H2020-MSCA","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G3477743816","display_name":null,"funder_award_id":"H2020-MSCA-RISE","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G526235227","display_name":null,"funder_award_id":"777911","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G6059518138","display_name":null,"funder_award_id":"MSCA-RISE-2017-777911","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G6131758448","display_name":null,"funder_award_id":"MTM2016-77278-P (FEDER)","funder_id":"https://openalex.org/F4320326262","funder_display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a"},{"id":"https://openalex.org/G683931746","display_name":null,"funder_award_id":"H2020","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7015168732","display_name":null,"funder_award_id":"H2020-MSCA-RISE-2017","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G8646112941","display_name":null,"funder_award_id":"H2020-MSCA-RISE-2017-777911","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320322864","display_name":"Isfahan University of Technology","ror":"https://ror.org/00af3sa43"},{"id":"https://openalex.org/F4320326262","display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a","ror":"https://ror.org/03sv46s19"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3017264843.pdf","grobid_xml":"https://content.openalex.org/works/W3017264843.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W589366791","https://openalex.org/W1969156705","https://openalex.org/W1969975546","https://openalex.org/W1974942353","https://openalex.org/W1987019566","https://openalex.org/W1987344369","https://openalex.org/W1989008630","https://openalex.org/W1997495989","https://openalex.org/W1998527012","https://openalex.org/W1998762702","https://openalex.org/W2009654833","https://openalex.org/W2019143828","https://openalex.org/W2030527508","https://openalex.org/W2036025652","https://openalex.org/W2044413922","https://openalex.org/W2052155732","https://openalex.org/W2059682210","https://openalex.org/W2060177655","https://openalex.org/W2065540527","https://openalex.org/W2340218647","https://openalex.org/W2521317762","https://openalex.org/W2913430022","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2051439117","https://openalex.org/W4388297534","https://openalex.org/W1673883441","https://openalex.org/W4298109871","https://openalex.org/W2313188567","https://openalex.org/W4248124207","https://openalex.org/W2087320822","https://openalex.org/W2996059826","https://openalex.org/W2083477739","https://openalex.org/W2089966216"],"abstract_inverted_index":{"Consider":[0],"the":[1,23,29,37,49,66,80,97,101],"class":[2,82],"of":[3,36,83,104],"reversible":[4],"quadratic":[5,15,84],"systems":[6,18,44,87],"[Formula:":[7,11,25,31,51,55,60,116],"see":[8,12,26,32,52,56,61,117],"text]":[9,27,33,53,62,118],"with":[10,54],"text].":[13,57],"These":[14,43],"polynomial":[16,85],"differential":[17,86],"have":[19],"a":[20],"center":[21,102],"at":[22,90],"point":[24],"and":[28],"circle":[30],"is":[34],"one":[35],"periodic":[38,98],"orbits":[39,99],"surrounding":[40,100],"this":[41,75,110],"center.":[42],"can":[45,88],"be":[46],"written":[47],"into":[48],"form":[50],"For":[58],"all":[59],"we":[63],"prove":[64],"that":[65,105],"averaging":[67],"theory":[68],"up":[69],"to":[70,74,108],"seventh":[71],"order":[72],"applied":[73],"last":[76],"system":[77],"perturbed":[78],"inside":[79],"whole":[81],"produce":[89],"most":[91],"two":[92],"limit":[93],"cycles":[94],"bifurcating":[95],"from":[96],"(0,0)":[103],"system.":[106],"Up":[107],"now":[109],"result":[111],"was":[112],"only":[113],"known":[114],"for":[115],"(see":[119],"Li,":[120],"2002;":[121],"Liu,":[122],"2012).":[123]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}