{"id":"https://openalex.org/W2077398926","doi":"https://doi.org/10.1142/s0218127412501891","title":"LIMIT CYCLE BIFURCATIONS NEAR A DOUBLE HOMOCLINIC LOOP WITH A NILPOTENT SADDLE","display_name":"LIMIT CYCLE BIFURCATIONS NEAR A DOUBLE HOMOCLINIC LOOP WITH A NILPOTENT SADDLE","publication_year":2012,"publication_date":"2012-08-01","ids":{"openalex":"https://openalex.org/W2077398926","doi":"https://doi.org/10.1142/s0218127412501891","mag":"2077398926"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127412501891","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127412501891","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/A5034144161","display_name":"Junmin Yang","orcid":"https://orcid.org/0000-0002-1627-0035"},"institutions":[{"id":"https://openalex.org/I94611258","display_name":"Hebei Normal University","ror":"https://ror.org/004rbbw49","country_code":"CN","type":"education","lineage":["https://openalex.org/I94611258"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JUNMIN YANG","raw_affiliation_strings":["College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, P. R. China","institution_ids":["https://openalex.org/I94611258"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041509169","display_name":"Dongmei Xiao","orcid":"https://orcid.org/0000-0002-6330-578X"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"DONGMEI XIAO","raw_affiliation_strings":["Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, P. R. China","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9349,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.90232757,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"22","issue":"08","first_page":"1250189","last_page":"1250189"},"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":0.9677000045776367,"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/T11844","display_name":"Lipid metabolism and biosynthesis","score":0.9218000173568726,"subfield":{"id":"https://openalex.org/subfields/1303","display_name":"Biochemistry"},"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/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9139788746833801},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8030086755752563},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.7214102149009705},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.7194333076477051},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5952427983283997},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5691615343093872},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.5623583793640137},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5324704647064209},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5192420482635498},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.46470537781715393},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.44756168127059937},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4376758635044098},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.28503739833831787},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21928200125694275},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15003305673599243},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08188331127166748},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05386912822723389}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9139788746833801},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8030086755752563},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.7214102149009705},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.7194333076477051},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5952427983283997},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5691615343093872},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.5623583793640137},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5324704647064209},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5192420482635498},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.46470537781715393},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.44756168127059937},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4376758635044098},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.28503739833831787},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21928200125694275},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15003305673599243},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08188331127166748},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05386912822723389},{"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/s0218127412501891","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127412501891","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":14,"referenced_works":["https://openalex.org/W1584825470","https://openalex.org/W1607000426","https://openalex.org/W1977739599","https://openalex.org/W1979832219","https://openalex.org/W1995731991","https://openalex.org/W1998762702","https://openalex.org/W2001428827","https://openalex.org/W2019313558","https://openalex.org/W2031704035","https://openalex.org/W2042498362","https://openalex.org/W2049815318","https://openalex.org/W2083318543","https://openalex.org/W2097813893","https://openalex.org/W2142664960"],"related_works":["https://openalex.org/W2890492950","https://openalex.org/W3115184012","https://openalex.org/W2010606039","https://openalex.org/W352136236","https://openalex.org/W1999123830","https://openalex.org/W2042800579","https://openalex.org/W944345475","https://openalex.org/W2112325763","https://openalex.org/W2373389541","https://openalex.org/W2166401415"],"abstract_inverted_index":{"Homoclinic":[0],"bifurcation":[1,9,116],"is":[2,180],"a":[3,14,18,23,41,47,70,75,98,118,124,159,177,183,193],"difficult":[4],"and":[5,57,90,142,191],"important":[6],"topic":[7],"of":[8,34,132,161,174,196,200,206],"theory.":[10],"As":[11],"we":[12,85,112],"know,":[13],"general":[15,99,139,178],"theory":[16,100,179],"for":[17,138,146,170],"homoclinic":[19,43,71,120,172],"loop":[20,44,72,121,163,173],"passing":[21,45,73,122],"through":[22,46,74,123],"hyperbolic":[24,48],"saddle":[25,49,77,126],"was":[26,50,101],"established":[27,103],"by":[28,60,87,127],"[Roussarie,":[29],"1986].":[30],"Then":[31],"the":[32,95,129,133,144,147,162,171,197],"method":[33],"stability-changing":[35],"to":[36,150],"find":[37,192],"limit":[38,114,156,201],"cycles":[39,157,202],"near":[40,117],"double":[42,119],"given":[51],"in":[52,104,158],"[Han":[53,61],"&":[54,66],"Chen,":[55],"2000],":[56],"further":[58],"developed":[59],"et":[62,106],"al.,":[63,107],"2003;":[64],"Han":[65],"Zhu,":[67],"2007].":[68],"For":[69,94],"nilpotent":[76,125],"there":[78],"are":[79],"essentially":[80],"two":[81],"different":[82,166],"cases,":[83],"which":[84],"distinguish":[86],"cuspidal":[88,96],"type":[89,97],"smooth":[91,175],"type,":[92,176],"respectively.":[93],"recently":[102],"[Zang":[105],"2008].":[108],"In":[109,168],"this":[110],"paper,":[111],"consider":[113,187],"cycle":[115],"studying":[128],"analytical":[130],"property":[131],"first":[134],"order":[135],"Melnikov":[136],"functions":[137],"near-Hamiltonian":[140],"systems":[141,190],"obtain":[143],"conditions":[145],"perturbed":[148],"system":[149],"have":[151],"8,":[152],"10":[153],"or":[154],"12":[155],"neighborhood":[160],"with":[164],"seven":[165],"distributions.":[167],"particular,":[169],"obtained":[181],"as":[182,203],"consequence.":[184],"We":[185],"finally":[186],"some":[188],"polynomial":[189],"lower":[194],"bound":[195],"maximal":[198],"number":[199],"an":[204],"application":[205],"our":[207],"main":[208],"results.":[209]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}