{"id":"https://openalex.org/W4408844656","doi":"https://doi.org/10.1142/s0218127425500701","title":"On the Number of Limit Cycles in Two Classes of Polynomial Differential Systems","display_name":"On the Number of Limit Cycles in Two Classes of Polynomial Differential Systems","publication_year":2025,"publication_date":"2025-03-25","ids":{"openalex":"https://openalex.org/W4408844656","doi":"https://doi.org/10.1142/s0218127425500701"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127425500701","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425500701","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/A5086578009","display_name":"Yiying Bao","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yu Bao","raw_affiliation_strings":["School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai Campus, Zhuhai 519082, P. R. China"],"raw_orcid":"https://orcid.org/0009-0008-6780-2290","affiliations":[{"raw_affiliation_string":"School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai Campus, Zhuhai 519082, P. R. China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100622914","display_name":"Shimin Li","orcid":null},"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":"Shimin Li","raw_affiliation_strings":["Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-1695-0097","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/A5046015548","display_name":"Jaume Llibre","orcid":"https://orcid.org/0000-0002-9511-5999"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jaume Llibre","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9511-5999","affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101834950","display_name":"Yulin Zhao","orcid":"https://orcid.org/0000-0002-4179-2409"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yulin Zhao","raw_affiliation_strings":["School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai Campus, Zhuhai 519082, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-4179-2409","affiliations":[{"raw_affiliation_string":"School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai Campus, Zhuhai 519082, P. R. China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5086578009"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09905325,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"06","first_page":null,"last_page":null},"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":0.9972000122070312,"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":0.9972000122070312,"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/T13935","display_name":"Mathematical Control Systems and Analysis","score":0.9745000004768372,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7265120148658752},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.693449854850769},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6389120817184448},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5758903622627258},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5436957478523254},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3681674301624298},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3547150492668152},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18757379055023193},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.06941795349121094}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7265120148658752},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.693449854850769},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6389120817184448},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5758903622627258},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5436957478523254},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3681674301624298},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3547150492668152},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18757379055023193},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.06941795349121094}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127425500701","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425500701","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"},{"id":"pmh:oai:ddd.uab.cat:312575","is_oa":false,"landing_page_url":"https://ddd.uab.cat/record/312575","pdf_url":null,"source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2335697406","display_name":null,"funder_award_id":"12071091","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2391038068","display_name":null,"funder_award_id":"PID2022-136613NB-100","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"},{"id":"https://openalex.org/G2749646526","display_name":null,"funder_award_id":"12371183","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4110412463","display_name":null,"funder_award_id":"2021SGR00113","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G4529452710","display_name":null,"funder_award_id":"2022A1515012105","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320331146","display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","ror":null},{"id":"https://openalex.org/F4320334830","display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca","ror":"https://ror.org/01n4pqe45"},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1556059214","https://openalex.org/W2001672492","https://openalex.org/W2008423115","https://openalex.org/W2020278866","https://openalex.org/W2034788479","https://openalex.org/W2039977986","https://openalex.org/W2049139319","https://openalex.org/W2049815318","https://openalex.org/W2078164200","https://openalex.org/W2092265840","https://openalex.org/W2158334808","https://openalex.org/W2353647791","https://openalex.org/W2584984113","https://openalex.org/W2810279415","https://openalex.org/W2998766904","https://openalex.org/W4230976486"],"related_works":["https://openalex.org/W4388297534","https://openalex.org/W2051439117","https://openalex.org/W1673883441","https://openalex.org/W4298109871","https://openalex.org/W2313188567","https://openalex.org/W4248124207","https://openalex.org/W2083477739","https://openalex.org/W2089966216","https://openalex.org/W2017930464","https://openalex.org/W2017252923"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,21],"two":[4],"classes":[5],"of":[6,33,36,46],"polynomial":[7,38],"differential":[8,16,39],"systems":[9,17,40],"that":[10],"are":[11],"generalized":[12],"rigid":[13],"systems,":[14],"i.e.":[15],"whose":[18],"orbits":[19],"rotate":[20],"a":[22],"constant":[23],"angular":[24],"velocity.":[25],"We":[26],"give":[27],"bounds":[28],"for":[29],"the":[30,43],"maximum":[31],"number":[32],"limit":[34],"cycles":[35],"such":[37],"provided":[41],"by":[42],"averaging":[44],"theory":[45],"first-order.":[47]},"counts_by_year":[],"updated_date":"2025-12-19T19:40:27.379048","created_date":"2025-10-10T00:00:00"}