{"id":"https://openalex.org/W1995731991","doi":"https://doi.org/10.1142/s0218127408022226","title":"LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER","display_name":"LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER","publication_year":2008,"publication_date":"2008-10-01","ids":{"openalex":"https://openalex.org/W1995731991","doi":"https://doi.org/10.1142/s0218127408022226","mag":"1995731991"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127408022226","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408022226","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, Guilin Rd. 100, Shanghai 200234, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Guilin Rd. 100, Shanghai 200234, P. R. China","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042517297","display_name":"Jiao Jiang","orcid":"https://orcid.org/0000-0001-5273-9032"},"institutions":[{"id":"https://openalex.org/I96733725","display_name":"Shanghai Maritime University","ror":"https://ror.org/04z7qrj66","country_code":"CN","type":"education","lineage":["https://openalex.org/I96733725"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JIAO JIANG","raw_affiliation_strings":["Department of Mathematics, Shanghai Maritime University, Shanghai 200135, P. R. China","Department of Mathematics , Shanghai Maritime University , Shanghai 200135, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Maritime University, Shanghai 200135, P. R. China","institution_ids":["https://openalex.org/I96733725"]},{"raw_affiliation_string":"Department of Mathematics , Shanghai Maritime University , Shanghai 200135, P.R. China","institution_ids":["https://openalex.org/I96733725"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036182391","display_name":"Huaiping Zhu","orcid":"https://orcid.org/0000-0003-2718-595X"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"HUAIPING ZHU","raw_affiliation_strings":["Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada","Department of Mathematics and Statistics , York University , Toronto, Ontario , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada","institution_ids":["https://openalex.org/I192455969"]},{"raw_affiliation_string":"Department of Mathematics and Statistics , York University , Toronto, Ontario , Canada","institution_ids":["https://openalex.org/I192455969"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8204,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.82672421,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"10","first_page":"3013","last_page":"3027"},"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":0.9776999950408936,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9388999938964844,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.7992278933525085},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7531343698501587},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7309876680374146},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.7088040113449097},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.6321699619293213},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.5738736391067505},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.5563689470291138},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5555065870285034},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5005302429199219},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.4989664554595947},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.48685115575790405},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4701573848724365},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.4651775062084198},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.43460261821746826},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.4291324019432068},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.419354647397995},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.265646755695343},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19529294967651367},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10413715243339539},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09296274185180664}],"concepts":[{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.7992278933525085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7531343698501587},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7309876680374146},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.7088040113449097},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.6321699619293213},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.5738736391067505},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.5563689470291138},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5555065870285034},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5005302429199219},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4989664554595947},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.48685115575790405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4701573848724365},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.4651775062084198},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.43460261821746826},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.4291324019432068},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.419354647397995},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.265646755695343},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19529294967651367},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10413715243339539},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09296274185180664},{"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/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127408022226","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408022226","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":23,"referenced_works":["https://openalex.org/W1963615000","https://openalex.org/W1967179029","https://openalex.org/W1968938958","https://openalex.org/W1976690062","https://openalex.org/W1998762702","https://openalex.org/W2002994865","https://openalex.org/W2003785155","https://openalex.org/W2004611416","https://openalex.org/W2012985567","https://openalex.org/W2014760113","https://openalex.org/W2019313558","https://openalex.org/W2024356403","https://openalex.org/W2032833409","https://openalex.org/W2034022724","https://openalex.org/W2040736253","https://openalex.org/W2049815318","https://openalex.org/W2054609165","https://openalex.org/W2057248748","https://openalex.org/W2075420560","https://openalex.org/W2113034974","https://openalex.org/W2792049198","https://openalex.org/W4237970627","https://openalex.org/W4293079168"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W2775656422","https://openalex.org/W2325048728","https://openalex.org/W56905705","https://openalex.org/W2560127293","https://openalex.org/W4245057904","https://openalex.org/W2803928976","https://openalex.org/W2978098199","https://openalex.org/W3042510364","https://openalex.org/W2003334682"],"abstract_inverted_index":{"As":[0],"we":[1,39,80],"know,":[2],"Hopf":[3],"bifurcation":[4,10,23,84,90],"is":[5,108],"an":[6,57],"important":[7],"part":[8],"of":[9,12,26],"theory":[11],"dynamical":[13],"systems.":[14],"Almost":[15],"all":[16],"known":[17],"works":[18],"are":[19],"concerned":[20],"with":[21,69],"the":[22,36,46,60,66,74,87,92],"and":[24],"number":[25],"limit":[27,88,105],"cycles":[28,106],"near":[29,65,91],"a":[30,41,52,70,82,100],"nondegenerate":[31],"focus":[32],"or":[33],"center.":[34,54,94],"In":[35],"present":[37],"paper,":[38],"study":[40],"general":[42],"near-Hamiltonian":[43],"system":[44,50,102],"on":[45],"plane":[47],"whose":[48],"unperturbed":[49],"has":[51],"nilpotent":[53,93],"We":[55],"obtain":[56,81],"expansion":[58],"for":[59,73],"first":[61,75],"order":[62],"Melnikov":[63],"function":[64],"center":[67],"together":[68],"computing":[71],"method":[72],"coefficients.":[76],"Using":[77],"these":[78],"coefficients,":[79],"new":[83],"theorem":[85],"concerning":[86],"cycle":[89],"An":[95],"interesting":[96],"application":[97],"example":[98],"&amp;":[99,107],"cubic":[101],"having":[103],"five":[104],"also":[109],"presented.":[110]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
