{"id":"https://openalex.org/W2152994297","doi":"https://doi.org/10.1142/s0218127413501721","title":"BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTERS FOR A QUARTIC SYSTEM","display_name":"BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTERS FOR A QUARTIC SYSTEM","publication_year":2013,"publication_date":"2013-10-01","ids":{"openalex":"https://openalex.org/W2152994297","doi":"https://doi.org/10.1142/s0218127413501721","mag":"2152994297"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413501721","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413501721","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/A5020491525","display_name":"Wentao Huang","orcid":"https://orcid.org/0000-0002-6420-3232"},"institutions":[{"id":"https://openalex.org/I4210155828","display_name":"Hezhou University","ror":"https://ror.org/04nm9ed20","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210155828"]},{"id":"https://openalex.org/I5343935","display_name":"Guilin University of Electronic Technology","ror":"https://ror.org/05arjae42","country_code":"CN","type":"education","lineage":["https://openalex.org/I5343935"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"WENTAO HUANG","raw_affiliation_strings":["Department of Mathematics, Hezhou University, Hezhou 542800, P. R. China","Guangxi Key Laboratory of Trusted Software, School of Computing Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hezhou University, Hezhou 542800, P. R. China","institution_ids":["https://openalex.org/I4210155828"]},{"raw_affiliation_string":"Guangxi Key Laboratory of Trusted Software, School of Computing Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004, P. R. China","institution_ids":["https://openalex.org/I5343935"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077364922","display_name":"Aiyong Chen","orcid":"https://orcid.org/0000-0001-8409-1701"},"institutions":[{"id":"https://openalex.org/I5343935","display_name":"Guilin University of Electronic Technology","ror":"https://ror.org/05arjae42","country_code":"CN","type":"education","lineage":["https://openalex.org/I5343935"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"AIYONG CHEN","raw_affiliation_strings":["School of Computing Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004, P. R. China","institution_ids":["https://openalex.org/I5343935"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076774278","display_name":"Qiujin Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I5343935","display_name":"Guilin University of Electronic Technology","ror":"https://ror.org/05arjae42","country_code":"CN","type":"education","lineage":["https://openalex.org/I5343935"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"QIUJIN XU","raw_affiliation_strings":["Vocational Technology Institute, Guilin University of Electronic Technology, Guangxi Beihai 536000, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vocational Technology Institute, Guilin University of Electronic Technology, Guangxi Beihai 536000, P. R. China","institution_ids":["https://openalex.org/I5343935"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020491525"],"corresponding_institution_ids":["https://openalex.org/I4210155828","https://openalex.org/I5343935"],"apc_list":null,"apc_paid":null,"fwci":1.3152,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.80689832,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"23","issue":"10","first_page":"1350172","last_page":"1350172"},"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":0.9028000235557556,"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/quartic-function","display_name":"Quartic function","score":0.9564015865325928},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.7807382345199585},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.7296738624572754},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6658976674079895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6650095582008362},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.5669881105422974},{"id":"https://openalex.org/keywords/singular-point-of-a-curve","display_name":"Singular point of a curve","score":0.511978268623352},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5112171173095703},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.48864060640335083},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4632832407951355},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4340234100818634},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.4257563054561615},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4120987057685852},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.33049696683883667},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32094040513038635},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18661227822303772},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18277853727340698},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11816549301147461},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0495685338973999}],"concepts":[{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.9564015865325928},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7807382345199585},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.7296738624572754},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6658976674079895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6650095582008362},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.5669881105422974},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.511978268623352},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5112171173095703},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.48864060640335083},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4632832407951355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4340234100818634},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4257563054561615},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4120987057685852},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.33049696683883667},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32094040513038635},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18661227822303772},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18277853727340698},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11816549301147461},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0495685338973999},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127413501721","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413501721","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":[{"id":"https://metadata.un.org/sdg/11","score":0.6700000166893005,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W17819749","https://openalex.org/W1980131874","https://openalex.org/W1980482575","https://openalex.org/W1986378144","https://openalex.org/W2003004883","https://openalex.org/W2006620620","https://openalex.org/W2028888525","https://openalex.org/W2046858619","https://openalex.org/W2049815318","https://openalex.org/W2053496265","https://openalex.org/W2086054590","https://openalex.org/W2094231262","https://openalex.org/W2113018613","https://openalex.org/W2129875234","https://openalex.org/W2167513707","https://openalex.org/W2366782616"],"related_works":["https://openalex.org/W17819749","https://openalex.org/W1552240070","https://openalex.org/W2378176293","https://openalex.org/W2371429222","https://openalex.org/W2364977425","https://openalex.org/W2349735028","https://openalex.org/W2353430195","https://openalex.org/W110415256","https://openalex.org/W1964764695","https://openalex.org/W2357904239"],"abstract_inverted_index":{"For":[0],"a":[1,19,55,72,81],"quartic":[2,73],"polynomial":[3],"system":[4,46,74],"we":[5,26],"investigate":[6],"bifurcations":[7],"of":[8,57,63,71],"limit":[9,52,77],"cycles":[10,53,78],"and":[11,89],"obtain":[12],"conditions":[13,30,91],"for":[14,31,92],"the":[15,22,29,32,36,45,58,61,68,87,93],"origin":[16,33,94],"to":[17,34,95],"be":[18,35,96],"center.":[20,99],"Computing":[21],"singular":[23],"point":[24],"values":[25],"find":[27],"also":[28,85],"eighth":[37],"order":[38],"fine":[39,82],"focus.":[40,83],"It":[41],"is":[42,67],"proven":[43],"that":[44],"can":[47],"have":[48],"eight":[49,76],"small":[50],"amplitude":[51],"in":[54],"neighborhood":[56],"origin.":[59],"To":[60],"best":[62],"our":[64],"knowledge,":[65],"this":[66],"first":[69],"example":[70],"with":[75],"bifurcated":[79],"from":[80],"We":[84],"give":[86],"sufficient":[88],"necessary":[90],"an":[97],"isochronous":[98]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}