{"id":"https://openalex.org/W3042606133","doi":"https://doi.org/10.1109/access.2020.3009204","title":"Analytical Bifurcation Tree of Period-1 to Period-4 Motions in a 3-D Brushless DC Motor With Voltage Disturbance","display_name":"Analytical Bifurcation Tree of Period-1 to Period-4 Motions in a 3-D Brushless DC Motor With Voltage Disturbance","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3042606133","doi":"https://doi.org/10.1109/access.2020.3009204","mag":"3042606133"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.3009204","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3009204","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09139974.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09139974.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101836213","display_name":"Zhaobo Chen","orcid":"https://orcid.org/0000-0001-7693-6014"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaobo Chen","raw_affiliation_strings":["Department of Mechatronics Engineering, Harbin Institute of Technology, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechatronics Engineering, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047983461","display_name":"Yeyin Xu","orcid":"https://orcid.org/0000-0001-7379-6976"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yeyin Xu","raw_affiliation_strings":["Department of Mechatronics Engineering, Harbin Institute of Technology, Harbin, China"],"raw_orcid":"https://orcid.org/0000-0001-7379-6976","affiliations":[{"raw_affiliation_string":"Department of Mechatronics Engineering, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035523453","display_name":"Jiayang Ying","orcid":"https://orcid.org/0000-0002-6372-4036"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiayang Ying","raw_affiliation_strings":["Department of Mechatronics Engineering, Harbin Institute of Technology, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechatronics Engineering, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.1041,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.42387222,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"8","issue":null,"first_page":"129613","last_page":"129625"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10278","display_name":"Electric Motor Design and Analysis","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10278","display_name":"Electric Motor Design and Analysis","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11602","display_name":"Magnetic Bearings and Levitation Dynamics","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11222","display_name":"Magnetic Properties and Applications","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7061429023742676},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6997786164283752},{"id":"https://openalex.org/keywords/dc-motor","display_name":"DC motor","score":0.692169725894928},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6680242419242859},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.6427178382873535},{"id":"https://openalex.org/keywords/harmonic-balance","display_name":"Harmonic balance","score":0.49189281463623047},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43531981110572815},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.4118395149707794},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.35949522256851196},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34830325841903687},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3050518035888672},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.19374528527259827},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10354679822921753},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.09410613775253296}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7061429023742676},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6997786164283752},{"id":"https://openalex.org/C76684090","wikidata":"https://www.wikidata.org/wiki/Q3842034","display_name":"DC motor","level":2,"score":0.692169725894928},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6680242419242859},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.6427178382873535},{"id":"https://openalex.org/C121758426","wikidata":"https://www.wikidata.org/wiki/Q5659248","display_name":"Harmonic balance","level":3,"score":0.49189281463623047},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43531981110572815},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4118395149707794},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35949522256851196},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34830325841903687},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3050518035888672},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.19374528527259827},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10354679822921753},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.09410613775253296},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2020.3009204","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3009204","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09139974.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b53eb63a8748452cb3e84c2c7878b297","is_oa":true,"landing_page_url":"https://doaj.org/article/b53eb63a8748452cb3e84c2c7878b297","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 8, Pp 129613-129625 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.3009204","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3009204","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09139974.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3042606133.pdf","grobid_xml":"https://content.openalex.org/works/W3042606133.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W89702005","https://openalex.org/W589194659","https://openalex.org/W1492106411","https://openalex.org/W1993438976","https://openalex.org/W2050683487","https://openalex.org/W2062404349","https://openalex.org/W2071718065","https://openalex.org/W2102413718","https://openalex.org/W2117409170","https://openalex.org/W2117648531","https://openalex.org/W2118207610","https://openalex.org/W2269334692","https://openalex.org/W2487464852","https://openalex.org/W2500762073","https://openalex.org/W2586993623","https://openalex.org/W2621662934","https://openalex.org/W2908010345"],"related_works":["https://openalex.org/W2158091184","https://openalex.org/W2382140662","https://openalex.org/W2063574925","https://openalex.org/W3179723297","https://openalex.org/W197510432","https://openalex.org/W3021098778","https://openalex.org/W4310236371","https://openalex.org/W3148401657","https://openalex.org/W2103328473","https://openalex.org/W2990794161"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,16,22,33,40,55,89,93,100,106,122,135,145,152],"bifurcation":[4,153],"trees":[5,70,154],"of":[6,9,32,43,45,54,71,74,88,92,102,105,112,121,134,144,155],"analytical":[7,52,72,90,136,156],"solutions":[8,53,73,91,137],"a":[10,64,118],"3-D":[11,34,56,94,146],"brushless":[12,35,57,95,147],"DC":[13],"motor":[14,36,58,96,148],"with":[15,138],"voltage":[17],"disturbance":[18],"are":[19,59,83,97,115,130,149],"obtained":[20],"through":[21,151],"generalized":[23],"harmonic":[24],"balance":[25],"method.":[26],"The":[27,141],"electrical":[28],"and":[29,50,78,86],"mechanical":[30],"model":[31],"is":[37],"transformed":[38],"to":[39,76,80],"dynamic":[41,108],"system":[42],"coefficients":[44],"finite":[46],"Fourier":[47,65],"series.":[48],"Stable":[49],"unstable":[51],"solved":[60],"based":[61],"on":[62],"such":[63],"series":[66],"coefficient":[67,107],"system.":[68,109],"Bifurcation":[69],"period-1":[75,79],"period-2":[77],"period-4":[81],"motions":[82,114],"achieved.":[84],"Stability":[85],"bifurcations":[87],"determined":[98],"by":[99],"eigenvalues":[101],"Jacobian":[103],"matrix":[104],"Frequency-amplitude":[110],"characteristics":[111],"periodic":[113],"presented":[116],"for":[117,132],"better":[119],"understanding":[120],"motion":[123],"complexity":[124],"in":[125],"frequency":[126],"domain.":[127],"Numerical":[128],"illustrations":[129],"completed":[131],"comparison":[133],"numerical":[139],"results.":[140],"complex":[142],"dynamics":[143],"exhibited":[150],"solutions.":[157]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}