{"id":"https://openalex.org/W3158581239","doi":"https://doi.org/10.1142/s021812742150067x","title":"The Number of Limit Cycles Bifurcating from a Degenerate Center of Piecewise Smooth Differential Systems","display_name":"The Number of Limit Cycles Bifurcating from a Degenerate Center of Piecewise Smooth Differential Systems","publication_year":2021,"publication_date":"2021-04-01","ids":{"openalex":"https://openalex.org/W3158581239","doi":"https://doi.org/10.1142/s021812742150067x","mag":"3158581239"},"language":"en","primary_location":{"id":"doi:10.1142/s021812742150067x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812742150067x","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/A5045264250","display_name":"Lijun Wei","orcid":"https://orcid.org/0000-0003-0620-3645"},"institutions":[{"id":"https://openalex.org/I163151501","display_name":"Hangzhou Normal University","ror":"https://ror.org/014v1mr15","country_code":"CN","type":"education","lineage":["https://openalex.org/I163151501"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lijun Wei","raw_affiliation_strings":["Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-0620-3645","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China","institution_ids":["https://openalex.org/I163151501"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009328791","display_name":"Yancong Xu","orcid":"https://orcid.org/0000-0002-0968-2234"},"institutions":[{"id":"https://openalex.org/I163151501","display_name":"Hangzhou Normal University","ror":"https://ror.org/014v1mr15","country_code":"CN","type":"education","lineage":["https://openalex.org/I163151501"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yancong Xu","raw_affiliation_strings":["Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China","institution_ids":["https://openalex.org/I163151501"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100368858","display_name":"Xiang Zhang","orcid":"https://orcid.org/0000-0002-4037-4272"},"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":"Xiang Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Key Laboratory of Scientific and Engineering Computing, (Ministry of Education), Shanghai Jiao Tong University, Shanghai 200240, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Key Laboratory of Scientific and Engineering Computing, (Ministry of Education), Shanghai Jiao Tong University, Shanghai 200240, P. R. China","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045264250"],"corresponding_institution_ids":["https://openalex.org/I163151501"],"apc_list":null,"apc_paid":null,"fwci":0.4105,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58583691,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"05","first_page":"2150067","last_page":"2150067"},"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":0.9043999910354614,"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/piecewise","display_name":"Piecewise","score":0.8100066184997559},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.753612756729126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7418806552886963},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.7074054479598999},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6661190986633301},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5632156133651733},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5545710325241089},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5520532131195068},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.49555718898773193},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4616910219192505},{"id":"https://openalex.org/keywords/center-of-mass","display_name":"Center of mass (relativistic)","score":0.4116884469985962},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3224393129348755},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2041771113872528},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12700611352920532},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.12502655386924744},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09252700209617615}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8100066184997559},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.753612756729126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7418806552886963},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.7074054479598999},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6661190986633301},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5632156133651733},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5545710325241089},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5520532131195068},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.49555718898773193},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4616910219192505},{"id":"https://openalex.org/C36185635","wikidata":"https://www.wikidata.org/wiki/Q17006925","display_name":"Center of mass (relativistic)","level":3,"score":0.4116884469985962},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3224393129348755},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2041771113872528},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12700611352920532},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.12502655386924744},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09252700209617615},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C47513753","wikidata":"https://www.wikidata.org/wiki/Q3502299","display_name":"Energy\u2013momentum relation","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021812742150067x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812742150067x","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/G1132569604","display_name":null,"funder_award_id":"LY20A010002","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G1925969676","display_name":"\u51e0\u7c7b\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u7684\u5c40\u90e8\u7ed3\u6784\u5206\u652f\u76f8\u5173\u95ee\u9898\u7814\u7a76","funder_award_id":"11671114","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4311261618","display_name":null,"funder_award_id":"2018QDL048","funder_id":"https://openalex.org/F4320337518","funder_display_name":"Illinois Program for Research in the Humanities, University of Illinois at Urbana-Champaign"},{"id":"https://openalex.org/G6938658389","display_name":"\u6709\u9650\u7ef4\u52a8\u529b\u7cfb\u7edf\u53ef\u79ef\u7684\u523b\u753b\u53ca\u5176\u52a8\u529b\u5b66\u7814\u7a76","funder_award_id":"11871334","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7807776135","display_name":null,"funder_award_id":"11671254","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8307908666","display_name":null,"funder_award_id":"11901144","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"},{"id":"https://openalex.org/F4320337518","display_name":"Illinois Program for Research in the Humanities, University of Illinois at Urbana-Champaign","ror":"https://ror.org/047426m28"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W201868982","https://openalex.org/W1973010592","https://openalex.org/W1974272814","https://openalex.org/W1980228211","https://openalex.org/W1980709212","https://openalex.org/W2001672492","https://openalex.org/W2002282594","https://openalex.org/W2002695016","https://openalex.org/W2008393500","https://openalex.org/W2013501206","https://openalex.org/W2016789606","https://openalex.org/W2032926717","https://openalex.org/W2037024940","https://openalex.org/W2038394595","https://openalex.org/W2039889532","https://openalex.org/W2053658423","https://openalex.org/W2054652000","https://openalex.org/W2066824120","https://openalex.org/W2079569562","https://openalex.org/W2092046534","https://openalex.org/W2094113013","https://openalex.org/W2128796982","https://openalex.org/W2133505353","https://openalex.org/W2240061011","https://openalex.org/W2321899621","https://openalex.org/W2336335035","https://openalex.org/W2343604074","https://openalex.org/W2493008392","https://openalex.org/W2525448883","https://openalex.org/W2559924465","https://openalex.org/W2951830236","https://openalex.org/W3102220905","https://openalex.org/W4230378422","https://openalex.org/W4293078920"],"related_works":["https://openalex.org/W2353039109","https://openalex.org/W4315588385","https://openalex.org/W3124638673","https://openalex.org/W2066153363","https://openalex.org/W2900100504","https://openalex.org/W2061564118","https://openalex.org/W4318566977","https://openalex.org/W4226164715","https://openalex.org/W3096660584","https://openalex.org/W3009543351"],"abstract_inverted_index":{"For":[0],"two":[1,104],"families":[2],"of":[3,30,38,45,122,125,134],"planar":[4],"piecewise":[5,97],"smooth":[6,98],"polynomial":[7,132],"differential":[8,99],"systems,":[9],"whose":[10],"unperturbed":[11,50],"system":[12],"has":[13],"a":[14,57],"degenerate":[15,63,126],"center":[16],"at":[17],"the":[18,22,27,35,39,46,78,84,109,114,119],"origin,":[19],"we":[20,102],"study":[21,68],"biggest":[23,115],"lower":[24,116],"bound":[25,117],"for":[26,95,107],"maximum":[28,120],"number":[29,121],"limit":[31,123],"cycles":[32,124],"bifurcating":[33],"from":[34,56],"periodic":[36],"orbits":[37],"center.":[40],"These":[41],"results":[42],"are":[43,77],"extensions":[44],"known":[47],"ones":[48],"on":[49,118],"nondegenerate":[51],"[Formula:":[52,64,127,136],"see":[53,65,128,137],"text]-center,":[54],"derived":[55],"nonsmooth":[58],"harmonic":[59],"oscillator":[60],"model,":[61],"to":[62],"text]-center.":[66],"Our":[67],"involves":[69],"some":[70],"new":[71],"computational":[72],"treatments.":[73],"The":[74],"main":[75],"tools":[76],"generalized":[79,85],"polar":[80,87],"coordinate":[81,88],"change":[82,89],"and":[83,112],"Lyapunov":[86],"together":[90],"with":[91],"an":[92],"averaging":[93,110],"theory":[94],"one-dimensional":[96],"equations.":[100],"Finally,":[101],"present":[103],"Maple":[105],"programs":[106],"computing":[108],"functions":[111],"consequently":[113],"text]-center":[129],"under":[130],"general":[131],"perturbations":[133],"degree":[135],"text].":[138]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
