{"id":"https://openalex.org/W2511124983","doi":"https://doi.org/10.1142/s0218127416501522","title":"Limit Cycle Bifurcation of Infinity and Degenerate Singular Point in Three-Dimensional Vector Field","display_name":"Limit Cycle Bifurcation of Infinity and Degenerate Singular Point in Three-Dimensional Vector Field","publication_year":2016,"publication_date":"2016-08-01","ids":{"openalex":"https://openalex.org/W2511124983","doi":"https://doi.org/10.1142/s0218127416501522","mag":"2511124983"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416501522","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501522","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/A5113003596","display_name":"Chaoxiong Du","orcid":null},"institutions":[{"id":"https://openalex.org/I206324368","display_name":"Shaoyang University","ror":"https://ror.org/03fx09x73","country_code":"CN","type":"education","lineage":["https://openalex.org/I206324368"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chaoxiong Du","raw_affiliation_strings":["Department of Mathematics, Hunan Shaoyang University, Shaoyang, Hunan 422000, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hunan Shaoyang University, Shaoyang, Hunan 422000, P. R. China","institution_ids":["https://openalex.org/I206324368"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047236489","display_name":"Yirong Liu","orcid":"https://orcid.org/0000-0002-6112-9815"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yirong Liu","raw_affiliation_strings":["School of Mathematics, Central South University, Changsha, Hunan 410083, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Central South University, Changsha, Hunan 410083, P. R. China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033652627","display_name":"Qi Zhang","orcid":"https://orcid.org/0000-0002-3917-525X"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qi Zhang","raw_affiliation_strings":["School of Mathematics, Central South University, Changsha, Hunan 410083, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Central South University, Changsha, Hunan 410083, P. R. China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113003596"],"corresponding_institution_ids":["https://openalex.org/I206324368"],"apc_list":null,"apc_paid":null,"fwci":0.5326,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68903323,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"26","issue":"09","first_page":"1650152","last_page":"1650152"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9804999828338623,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9681000113487244,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7135316133499146},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.7010007500648499},{"id":"https://openalex.org/keywords/singular-point-of-a-curve","display_name":"Singular point of a curve","score":0.6831945180892944},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.6602823138237},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6474539041519165},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.6192691326141357},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.6022212505340576},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5981705188751221},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5892289280891418},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.5752680897712708},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5498676896095276},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.5343614816665649},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.5027408599853516},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4755668044090271},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.29954421520233154},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2606261372566223},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.22688299417495728},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10834705829620361},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07554927468299866}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7135316133499146},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.7010007500648499},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.6831945180892944},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.6602823138237},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6474539041519165},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.6192691326141357},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6022212505340576},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5981705188751221},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5892289280891418},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.5752680897712708},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5498676896095276},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.5343614816665649},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.5027408599853516},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4755668044090271},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.29954421520233154},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2606261372566223},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.22688299417495728},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10834705829620361},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07554927468299866}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416501522","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501522","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":[],"awards":[{"id":"https://openalex.org/G1852334806","display_name":null,"funder_award_id":"11371373","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W899012284","https://openalex.org/W1588744197","https://openalex.org/W1973146098","https://openalex.org/W1982570268","https://openalex.org/W1986209500","https://openalex.org/W2000803234","https://openalex.org/W2001044557","https://openalex.org/W2001296105","https://openalex.org/W2005717825","https://openalex.org/W2006943190","https://openalex.org/W2021515729","https://openalex.org/W2032302555","https://openalex.org/W2076679125","https://openalex.org/W2093849459","https://openalex.org/W2178729250","https://openalex.org/W2273494358","https://openalex.org/W2347463901"],"related_works":["https://openalex.org/W2371429222","https://openalex.org/W2364977425","https://openalex.org/W2353430195","https://openalex.org/W1979887993","https://openalex.org/W2349735028","https://openalex.org/W2258032807","https://openalex.org/W3215671471","https://openalex.org/W110415256","https://openalex.org/W2511124983","https://openalex.org/W4292566988"],"abstract_inverted_index":{"Our":[0],"work":[1],"focuses":[2],"on":[3],"investigating":[4],"limit":[5,55,66,81,103,110],"cycle":[6],"bifurcation":[7],"for":[8,92,120],"infinity":[9],"and":[10,47,64,86],"a":[11,16,99,106],"degenerate":[12],"singular":[13,26],"point":[14],"of":[15,38,80,95,101,108],"fifth":[17],"degree":[18],"system":[19],"in":[20,124],"three-dimensional":[21,125],"vector":[22,126],"field.":[23],"By":[24],"using":[25],"value":[27],"method":[28],"to":[29],"compute":[30],"focal":[31,40],"values":[32,41],"carefully,":[33],"we":[34,51,76],"give":[35],"the":[36,39,45,62,73,78,84,87],"expressions":[37],"(Lyapunov":[42],"constants)":[43],"at":[44,48,57],"origin":[46,63,85],"infinity.":[49,71,88],"Moreover,":[50],"obtain":[52],"that":[53,98],"four":[54],"cycles":[56,67,82,104,111],"most":[58],"can":[59,68],"bifurcate":[60,69],"from":[61,70,83],"three":[65],"At":[72],"same":[74],"time,":[75],"show":[77],"structure":[79],"It":[89],"is":[90,117,130],"interesting":[91],"this":[93],"kind":[94],"nonlinear":[96],"phenomenon":[97],"string":[100,107],"large":[102],"encircle":[105],"small":[109],"by":[112],"simultaneous":[113],"Hopf":[114],"bifurcation,":[115],"which":[116],"hardly":[118],"seen":[119],"similar":[121],"published":[122],"results":[123],"field,":[127],"our":[128],"result":[129],"new.":[131]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}