{"id":"https://openalex.org/W4320017758","doi":"https://doi.org/10.1142/s0218127423500037","title":"Global Phase Portraits of the Quadratic Systems Having a Singular and Irreducible Invariant Curve of Degree 3","display_name":"Global Phase Portraits of the Quadratic Systems Having a Singular and Irreducible Invariant Curve of Degree 3","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4320017758","doi":"https://doi.org/10.1142/s0218127423500037"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127423500037","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423500037","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://upcommons.upc.edu/bitstreams/b50a8bc3-0624-4fc4-a172-cbc699ed6b1f/download","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":"J. Llibre","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona, Catalonia, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042281798","display_name":"Chara Pantazi","orcid":"https://orcid.org/0000-0002-4394-404X"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"C. Pantazi","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, (EPSEB), Av. Doctor Mara\u00f1\u00f3n, 44\u201350, 08028 Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, (EPSEB), Av. Doctor Mara\u00f1\u00f3n, 44\u201350, 08028 Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":1,"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":1.0874,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71099149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"33","issue":"01","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":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/T11435","display_name":"Polynomial and algebraic computation","score":0.9373000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9059000015258789,"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/phase-portrait","display_name":"Phase portrait","score":0.9615955352783203},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5981764793395996},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5553459525108337},{"id":"https://openalex.org/keywords/quadratic-differential","display_name":"Quadratic differential","score":0.5301854014396667},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5267131924629211},{"id":"https://openalex.org/keywords/invariant-theory","display_name":"Invariant theory","score":0.46382179856300354},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4622727334499359},{"id":"https://openalex.org/keywords/portrait","display_name":"Portrait","score":0.4406862258911133},{"id":"https://openalex.org/keywords/cubic-function","display_name":"Cubic function","score":0.4272609055042267},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3808554410934448},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2947842478752136},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23434299230575562},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.2262415885925293},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.143379807472229},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.12558621168136597},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.1253233253955841},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12072226405143738}],"concepts":[{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.9615955352783203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5981764793395996},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5553459525108337},{"id":"https://openalex.org/C2778433361","wikidata":"https://www.wikidata.org/wiki/Q7268358","display_name":"Quadratic differential","level":3,"score":0.5301854014396667},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5267131924629211},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.46382179856300354},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4622727334499359},{"id":"https://openalex.org/C162462552","wikidata":"https://www.wikidata.org/wiki/Q134307","display_name":"Portrait","level":2,"score":0.4406862258911133},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.4272609055042267},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3808554410934448},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2947842478752136},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23434299230575562},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2262415885925293},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.143379807472229},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.12558621168136597},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.1253233253955841},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12072226405143738},{"id":"https://openalex.org/C52119013","wikidata":"https://www.wikidata.org/wiki/Q50637","display_name":"Art history","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218127423500037","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423500037","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:upcommons.upc.edu:2117/384231","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/384231","pdf_url":"https://upcommons.upc.edu/bitstreams/b50a8bc3-0624-4fc4-a172-cbc699ed6b1f/download","source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:ddd.uab.cat:274781","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/274781","pdf_url":null,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:upcommons.upc.edu:2117/384231","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/384231","pdf_url":"https://upcommons.upc.edu/bitstreams/b50a8bc3-0624-4fc4-a172-cbc699ed6b1f/download","source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","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/G1549258023","display_name":null,"funder_award_id":"MSCA-RISE-2017-777911","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"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/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"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/G2548492180","display_name":null,"funder_award_id":"2017-777911","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G2628364946","display_name":null,"funder_award_id":"H2020","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3865843902","display_name":null,"funder_award_id":"PID-2021-122954NB-100","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G4126322094","display_name":null,"funder_award_id":"01100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G451917667","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G5175525644","display_name":null,"funder_award_id":"PID2019","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/G5859239756","display_name":null,"funder_award_id":"MSCA-RISE","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G5967599077","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"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/G618704488","display_name":null,"funder_award_id":"PID2019-104658GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G661330594","display_name":null,"funder_award_id":"00110","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6685425346","display_name":null,"funder_award_id":"0011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6770124728","display_name":null,"funder_award_id":"PID-2021-122954NB-100","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"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/G7073207951","display_name":null,"funder_award_id":"PID2019-104658GB-I00","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G7266728691","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7944295140","display_name":null,"funder_award_id":"H2020","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G8260616629","display_name":null,"funder_award_id":"011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8684520763","display_name":null,"funder_award_id":"PID2019","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","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/W4320017758.pdf","grobid_xml":"https://content.openalex.org/works/W4320017758.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1819700960","https://openalex.org/W1965582935","https://openalex.org/W1967532903","https://openalex.org/W1970193050","https://openalex.org/W1977702354","https://openalex.org/W1987019566","https://openalex.org/W1987399140","https://openalex.org/W1990026252","https://openalex.org/W2009654833","https://openalex.org/W2011741759","https://openalex.org/W2014480797","https://openalex.org/W2015308657","https://openalex.org/W2016207969","https://openalex.org/W2019178746","https://openalex.org/W2046895311","https://openalex.org/W2052155732","https://openalex.org/W2058335669","https://openalex.org/W2060163092","https://openalex.org/W2062487396","https://openalex.org/W2062666917","https://openalex.org/W2063970086","https://openalex.org/W2064089235","https://openalex.org/W2066476038","https://openalex.org/W2066699693","https://openalex.org/W2069076859","https://openalex.org/W2080225290","https://openalex.org/W2080740553","https://openalex.org/W2082055506","https://openalex.org/W2083063620","https://openalex.org/W2085197107","https://openalex.org/W2089729261","https://openalex.org/W2094232790","https://openalex.org/W2138155792","https://openalex.org/W2171300514","https://openalex.org/W2803954019","https://openalex.org/W3099453737","https://openalex.org/W3174964066","https://openalex.org/W4230688824","https://openalex.org/W4235472654","https://openalex.org/W4242340741"],"related_works":["https://openalex.org/W2767404218","https://openalex.org/W2895033324","https://openalex.org/W3099453737","https://openalex.org/W948244610","https://openalex.org/W3158797715","https://openalex.org/W4383106762","https://openalex.org/W4385445199","https://openalex.org/W4378213225","https://openalex.org/W4320017758","https://openalex.org/W4310282543"],"abstract_inverted_index":{"Any":[0],"singular":[1],"irreducible":[2],"cubic":[3,42],"curve":[4],"(or":[5],"simply,":[6],"cubic)":[7],"after":[8],"an":[9],"affine":[10],"transformation":[11],"can":[12],"be":[13],"written":[14],"as":[15],"either":[16],"[Formula:":[17,21,25,43,51],"see":[18,22,26,44,52],"text],":[19,23],"or":[20,24],"text].":[27,45],"We":[28,46,64],"classify":[29],"the":[30,40,67,117,122,135],"phase":[31,56,73,83,91,99,112,130],"portraits":[32,57,84,92,100,113,131],"of":[33,89,97,107,125,128],"all":[34,66],"quadratic":[35,60],"polynomial":[36,61],"differential":[37,62],"systems":[38,76],"having":[39],"invariant":[41],"prove":[47],"that":[48,109],"there":[49],"are":[50],"text]":[53],"different":[54],"topological":[55,72],"for":[58],"such":[59],"systems.":[63],"control":[65],"bifurcations":[68],"among":[69],"these":[70,90,98,111,129],"distinct":[71],"portraits.":[74],"These":[75],"have":[77,85,93,101,110],"no":[78],"limit":[79],"cycles.":[80],"Only":[81],"three":[82,96],"a":[86],"center,":[87],"19":[88],"one":[94],"polycycle,":[95],"two":[102],"polycycles.":[103],"The":[104],"maximum":[105,123],"number":[106,119,124],"separartices":[108],"is":[114,120,132,137],"26":[115],"and":[116,134],"minimum":[118,136],"nine,":[121],"canonical":[126],"regions":[127],"seven":[133],"three.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2023-02-11T00:00:00"}