{"id":"https://openalex.org/W2034821539","doi":"https://doi.org/10.1142/s0218127407019895","title":"BIFURCATION OF LIMIT CYCLES IN A FOURTH-ORDER NEAR-HAMILTONIAN SYSTEM","display_name":"BIFURCATION OF LIMIT CYCLES IN A FOURTH-ORDER NEAR-HAMILTONIAN SYSTEM","publication_year":2007,"publication_date":"2007-11-01","ids":{"openalex":"https://openalex.org/W2034821539","doi":"https://doi.org/10.1142/s0218127407019895","mag":"2034821539"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127407019895","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407019895","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/A5030649439","display_name":"Maoan Han","orcid":"https://orcid.org/0000-0001-8792-1256"},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"MAOAN HAN","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016695298","display_name":"Desheng Shang","orcid":null},"institutions":[{"id":"https://openalex.org/I119203015","display_name":"Shandong University of Technology","ror":"https://ror.org/02mr3ar13","country_code":"CN","type":"education","lineage":["https://openalex.org/I119203015"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"DESHENG SHANG","raw_affiliation_strings":["School of Mathematics and Information Science, Shandong University of Technology, Zibo 255049, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Shandong University of Technology, Zibo 255049, P. R. China","institution_ids":["https://openalex.org/I119203015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045214230","display_name":"Zheng Wang","orcid":"https://orcid.org/0000-0002-7726-0770"},"institutions":[{"id":"https://openalex.org/I119203015","display_name":"Shandong University of Technology","ror":"https://ror.org/02mr3ar13","country_code":"CN","type":"education","lineage":["https://openalex.org/I119203015"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"WANG ZHENG","raw_affiliation_strings":["School of Mathematics and Information Science, Shandong University of Technology, Zibo 255049, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Shandong University of Technology, Zibo 255049, P. R. China","institution_ids":["https://openalex.org/I119203015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100652002","display_name":"Pei Yu","orcid":"https://orcid.org/0000-0002-8848-0584"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"PEI YU","raw_affiliation_strings":["Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7696,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.81699905,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"17","issue":"11","first_page":"4117","last_page":"4144"},"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":0.9387999773025513,"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"}},{"id":"https://openalex.org/T10492","display_name":"Microtubule and mitosis dynamics","score":0.925000011920929,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7900872826576233},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.6964573264122009},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.691730260848999},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.672189474105835},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6441752910614014},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6398501396179199},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6011754274368286},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5360318422317505},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.5292258262634277},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.49389153718948364},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43472820520401},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.36747509241104126},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.254114031791687},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17650577425956726},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1606680154800415},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13077104091644287},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06639093160629272},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.05501517653465271}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7900872826576233},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.6964573264122009},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.691730260848999},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.672189474105835},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6441752910614014},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6398501396179199},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6011754274368286},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5360318422317505},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.5292258262634277},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.49389153718948364},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43472820520401},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.36747509241104126},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.254114031791687},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17650577425956726},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1606680154800415},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13077104091644287},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06639093160629272},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.05501517653465271},{"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/s0218127407019895","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407019895","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1976071188","https://openalex.org/W1982088565","https://openalex.org/W1988475523","https://openalex.org/W1990636372","https://openalex.org/W2001428827","https://openalex.org/W2012985567","https://openalex.org/W2017348434","https://openalex.org/W2029954120","https://openalex.org/W2034444332","https://openalex.org/W2039576666","https://openalex.org/W2042498362","https://openalex.org/W2044413922","https://openalex.org/W2049815318","https://openalex.org/W2078512508","https://openalex.org/W2148704323","https://openalex.org/W2160545686","https://openalex.org/W2168050314","https://openalex.org/W2224899793","https://openalex.org/W2372306478","https://openalex.org/W2389842380","https://openalex.org/W4237970627","https://openalex.org/W4248348571"],"related_works":["https://openalex.org/W17819749","https://openalex.org/W2373492234","https://openalex.org/W2050176506","https://openalex.org/W2039041609","https://openalex.org/W2945028955","https://openalex.org/W2353824527","https://openalex.org/W3098285481","https://openalex.org/W1552240070","https://openalex.org/W2364977425","https://openalex.org/W2353430195"],"abstract_inverted_index":{"This":[0,40],"paper":[1,86],"is":[2,48,61],"concerned":[3],"with":[4,14,37],"bifurcation":[5,18],"of":[6,56,80],"limit":[7,35,81],"cycles":[8,36,82],"in":[9,84],"a":[10],"fourth-order":[11],"near-Hamiltonian":[12],"system":[13,28],"quartic":[15],"perturbations.":[16],"By":[17],"theory,":[19],"proper":[20],"perturbations":[21],"are":[22],"given":[23],"to":[24],"show":[25],"that":[26,42,64,74],"the":[27,49,53,89],"may":[29],"have":[30],"20,":[31,45],"21":[32],"or":[33],"23":[34],"different":[38],"distributions.":[39],"shows":[41],"H(4)":[43,93],"\u2265":[44,66,76,94],"where":[46],"H(n)":[47],"Hilbert":[50],"number":[51,79],"for":[52,96],"second":[54],"part":[55],"Hilbert's":[57],"16th":[58],"problem.":[59],"It":[60],"well":[62],"known":[63],"H(2)":[65],"4,":[67],"and":[68],"it":[69],"has":[70],"been":[71],"recently":[72],"proved":[73],"H(3)":[75],"12.":[77],"The":[78],"obtained":[83],"this":[85],"greatly":[87],"improves":[88],"best":[90],"existing":[91],"result,":[92],"15,":[95],"fourth-degree":[97],"polynomial":[98],"planar":[99],"systems.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
