{"id":"https://openalex.org/W2220234366","doi":"https://doi.org/10.1142/s0218127415501357","title":"Center Problems and Limit Cycle Bifurcations in a Class of Quasi-Homogeneous Systems","display_name":"Center Problems and Limit Cycle Bifurcations in a Class of Quasi-Homogeneous Systems","publication_year":2015,"publication_date":"2015-09-01","ids":{"openalex":"https://openalex.org/W2220234366","doi":"https://doi.org/10.1142/s0218127415501357","mag":"2220234366"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127415501357","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415501357","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/A5018750678","display_name":"Yanqin Xiong","orcid":"https://orcid.org/0000-0003-2894-716X"},"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":"Yanqin Xiong","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/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":true,"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":"last","author":{"id":"https://openalex.org/A5050973119","display_name":"Yong Wang","orcid":"https://orcid.org/0000-0003-3654-2541"},"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":"Yong Wang","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"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030649439"],"corresponding_institution_ids":["https://openalex.org/I21945476"],"apc_list":null,"apc_paid":null,"fwci":2.6439,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.89266862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"25","issue":"10","first_page":"1550135","last_page":"1550135"},"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":0.9394999742507935,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9101999998092651,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/mathematics","display_name":"Mathematics","score":0.7675397992134094},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.7645602226257324},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.7499605417251587},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.6895710825920105},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6699966192245483},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5468931794166565},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.5410176515579224},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5038244128227234},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.49820995330810547},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48984596133232117},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4816545248031616},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44498705863952637},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40066075325012207},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37649935483932495},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.1883777379989624},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15911146998405457},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14872035384178162},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13043329119682312},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12082234025001526}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7675397992134094},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.7645602226257324},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.7499605417251587},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6895710825920105},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6699966192245483},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5468931794166565},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.5410176515579224},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5038244128227234},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.49820995330810547},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48984596133232117},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4816545248031616},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44498705863952637},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40066075325012207},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37649935483932495},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.1883777379989624},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15911146998405457},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14872035384178162},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13043329119682312},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12082234025001526},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/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/s0218127415501357","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415501357","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":17,"referenced_works":["https://openalex.org/W1968263269","https://openalex.org/W1968649987","https://openalex.org/W1982088565","https://openalex.org/W2007421134","https://openalex.org/W2025520707","https://openalex.org/W2027514662","https://openalex.org/W2032629612","https://openalex.org/W2036025652","https://openalex.org/W2041764074","https://openalex.org/W2041854671","https://openalex.org/W2045568967","https://openalex.org/W2054391745","https://openalex.org/W2074022343","https://openalex.org/W2081151351","https://openalex.org/W2092687100","https://openalex.org/W2962727226","https://openalex.org/W4211177484"],"related_works":["https://openalex.org/W2361025465","https://openalex.org/W2725010352","https://openalex.org/W2051439117","https://openalex.org/W4211076050","https://openalex.org/W2366033385","https://openalex.org/W220881879","https://openalex.org/W3156147585","https://openalex.org/W4307350259","https://openalex.org/W2240347535","https://openalex.org/W3164357037"],"abstract_inverted_index":{"In":[0],"this":[1,22],"paper,":[2],"we":[3,20,47],"first":[4,70],"classify":[5],"all":[6],"centers":[7],"of":[8,11,16,24,72],"a":[9,27,41,59],"class":[10],"quasi-homogeneous":[12],"polynomial":[13,29],"differential":[14,30],"systems":[15,25],"degree":[17],"5.":[18],"Then":[19],"extend":[21],"kind":[23],"to":[26,39,69],"generalized":[28],"system":[31,55],"and":[32,36],"provide":[33],"the":[34,44,49,62,65],"necessary":[35],"sufficient":[37],"conditions":[38],"have":[40],"center":[42,60],"at":[43,61],"origin.":[45],"Furthermore,":[46],"study":[48],"Poincar\u00e9":[50,66],"bifurcation":[51],"for":[52],"its":[53],"perturbed":[54],"as":[56],"it":[57],"has":[58],"origin,":[63],"find":[64],"cyclicity":[67],"up":[68],"order":[71],"\u03b5.":[73]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
