{"id":"https://openalex.org/W2118969162","doi":"https://doi.org/10.1142/s0218127411028544","title":"BIFURCATIONS OF LIMIT CYCLES CREATED BY A MULTIPLE NILPOTENT CRITICAL POINT OF PLANAR DYNAMICAL SYSTEMS","display_name":"BIFURCATIONS OF LIMIT CYCLES CREATED BY A MULTIPLE NILPOTENT CRITICAL POINT OF PLANAR DYNAMICAL SYSTEMS","publication_year":2011,"publication_date":"2011-02-01","ids":{"openalex":"https://openalex.org/W2118969162","doi":"https://doi.org/10.1142/s0218127411028544","mag":"2118969162"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127411028544","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411028544","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/A5047236489","display_name":"Yirong Liu","orcid":"https://orcid.org/0000-0002-6112-9815"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YIRONG LIU","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100599691","display_name":"Jibin Li","orcid":"https://orcid.org/0000-0003-4839-5956"},"institutions":[{"id":"https://openalex.org/I10660446","display_name":"Kunming University of Science and Technology","ror":"https://ror.org/00xyeez13","country_code":"CN","type":"education","lineage":["https://openalex.org/I10660446"]},{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JIBIN LI","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","School of Science, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"School of Science, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China","institution_ids":["https://openalex.org/I10660446"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1021,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.77470583,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"21","issue":"02","first_page":"497","last_page":"504"},"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":0.998199999332428,"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":0.998199999332428,"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/critical-point","display_name":"Critical point (mathematics)","score":0.7437309622764587},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7314909100532532},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6834496259689331},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6468983888626099},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6307011246681213},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.6249301433563232},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5955511331558228},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5689250230789185},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.5545312166213989},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5224010944366455},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5208418965339661},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.46710458397865295},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.43632882833480835},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43617331981658936},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.4127199053764343},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24992695450782776},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20768731832504272},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14432421326637268},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12067538499832153},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08269476890563965},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07345280051231384}],"concepts":[{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.7437309622764587},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7314909100532532},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6834496259689331},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6468983888626099},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6307011246681213},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.6249301433563232},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5955511331558228},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5689250230789185},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.5545312166213989},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5224010944366455},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5208418965339661},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.46710458397865295},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.43632882833480835},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43617331981658936},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4127199053764343},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24992695450782776},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20768731832504272},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14432421326637268},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12067538499832153},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08269476890563965},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07345280051231384},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127411028544","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411028544","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":[{"display_name":"Sustainable cities and communities","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1983540230","https://openalex.org/W2028287879","https://openalex.org/W2119673826","https://openalex.org/W2166490084","https://openalex.org/W4243371812"],"related_works":["https://openalex.org/W2039041609","https://openalex.org/W2094768441","https://openalex.org/W148729379","https://openalex.org/W2353430195","https://openalex.org/W2115351049","https://openalex.org/W2364977425","https://openalex.org/W4238806107","https://openalex.org/W2828044739","https://openalex.org/W2349735028","https://openalex.org/W2233462344"],"abstract_inverted_index":{"Bifurcations":[0],"of":[1,10,24,40,49],"limit":[2,25,65],"cycles":[3,26,66],"created":[4,27,61],"from":[5,19,28,67],"a":[6,56],"multiple":[7,42,47,71],"critical":[8,31,43,51,72],"point":[9,44],"planar":[11],"dynamical":[12],"systems":[13],"are":[14],"studied.":[15],"It":[16],"is":[17,74],"different":[18],"the":[20,38,41,46,50,68],"usual":[21],"Hopf":[22],"bifurcations":[23],"an":[29,54],"elementary":[30],"point.":[32,52],"This":[33],"bifurcation":[34],"phenomena":[35],"depends":[36],"on":[37],"stability":[39],"and":[45],"number":[48],"As":[53],"example,":[55],"cubic":[57],"system":[58],"which":[59],"can":[60],"four":[62],"small":[63],"amplitude":[64],"origin":[69],"(a":[70],"point)":[73],"given.":[75]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
