{"id":"https://openalex.org/W7225448686","doi":"https://doi.org/10.1016/j.chaos.2026.119443","title":"Bifurcation of limit cycles from a cubic center with a degenerated singular line","display_name":"Bifurcation of limit cycles from a cubic center with a degenerated singular line","publication_year":2026,"publication_date":"2026-11-07","ids":{"openalex":"https://openalex.org/W7225448686","doi":"https://doi.org/10.1016/j.chaos.2026.119443"},"language":"en","primary_location":{"id":"doi:10.1016/j.chaos.2026.119443","doi":"https://doi.org/10.1016/j.chaos.2026.119443","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.chaos.2026.119443","pdf_url":null,"source":{"id":"https://openalex.org/S70718007","display_name":"Chaos Solitons & Fractals","issn_l":"0960-0779","issn":["0960-0779","1873-2887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Chaos, Solitons & Fractals","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5078875844","display_name":"Peixing Yang","orcid":"https://orcid.org/0000-0001-6406-3594","observed_orcids":["https://orcid.org/0000-0001-6406-3594","https://orcid.org/0009-0006-1003-0993"]},"institutions":[{"id":"https://openalex.org/I137056471","display_name":"Nanjing University of Finance and Economics","ror":"https://ror.org/031y8am81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137056471"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peixing Yang","raw_affiliation_strings":["School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, 210023, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, 210023, PR China","institution_ids":["https://openalex.org/I137056471"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160171425","display_name":"Jiang Yu","orcid":null,"observed_orcids":[]},"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":"Jiang Yu","raw_affiliation_strings":["School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, 200240, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, 200240, PR China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5161237175","display_name":"Qianqian Zhao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I113992204","display_name":"Hebei University of Economics and Business","ror":"https://ror.org/05j1kc284","country_code":"CN","type":"education","lineage":["https://openalex.org/I113992204"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qianqian Zhao","raw_affiliation_strings":["College of Statistics and Mathematics, Hebei University of Economics and Business, Shijiazhuang, 050061, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Statistics and Mathematics, Hebei University of Economics and Business, Shijiazhuang, 050061, PR China","institution_ids":["https://openalex.org/I113992204"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5161237175"],"corresponding_institution_ids":["https://openalex.org/I113992204"],"apc_list":{"value":3970,"currency":"USD","value_usd":3970},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"214","issue":null,"first_page":"119443","last_page":"119443"},"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":0.9994999766349792,"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":0.9994999766349792,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bifurcation-of-limit-cycles","display_name":"bifurcation of limit cycles","score":0.9660000205039978},{"id":"https://openalex.org/keywords/melnikov-function","display_name":"Melnikov function","score":0.7450000047683716},{"id":"https://openalex.org/keywords/period-annulus","display_name":"period annulus","score":0.8640000224113464},{"id":"https://openalex.org/keywords/upper-bounds-on-limit-cycles","display_name":"upper bound of limit cycles","score":0.7400000095367432},{"id":"https://openalex.org/keywords/small-perturbations","display_name":"small perturbations","score":0.6940000057220459}],"concepts":[{"id":"https://openalex.org/C150936888","wikidata":"https://www.wikidata.org/wiki/Q4769748","display_name":"Annulus (botany)","level":2,"score":0.7929999828338623},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.743399977684021},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7156000137329102},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6797999739646912},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6370999813079834},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.616599977016449},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.5321000218391418},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4903999865055084},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4758000075817108},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4413999915122986},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.4027999937534332},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.3871000111103058},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35249999165534973},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.34709998965263367},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.3257000148296356},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30059999227523804},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C181154966","wikidata":"https://www.wikidata.org/wiki/Q2500406","display_name":"Li\u00e9nard equation","level":5,"score":0.27070000767707825},{"id":"https://openalex.org/C2781291010","wikidata":"https://www.wikidata.org/wiki/Q178580","display_name":"Period (music)","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.chaos.2026.119443","doi":"https://doi.org/10.1016/j.chaos.2026.119443","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.chaos.2026.119443","pdf_url":null,"source":{"id":"https://openalex.org/S70718007","display_name":"Chaos Solitons & Fractals","issn_l":"0960-0779","issn":["0960-0779","1873-2887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Chaos, Solitons & Fractals","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1997495989","https://openalex.org/W2016814271","https://openalex.org/W2020278866","https://openalex.org/W2029563761","https://openalex.org/W2039977986","https://openalex.org/W2041853839","https://openalex.org/W2049139319","https://openalex.org/W2051702433","https://openalex.org/W2074494063","https://openalex.org/W2092265840","https://openalex.org/W2143052212","https://openalex.org/W2160492379","https://openalex.org/W2972560302","https://openalex.org/W3087966516","https://openalex.org/W3089268694","https://openalex.org/W4390661902"],"related_works":["https://openalex.org/W3215671471","https://openalex.org/W4225380554","https://openalex.org/W2066296544","https://openalex.org/W4406350608","https://openalex.org/W2972560302","https://openalex.org/W4416162096","https://openalex.org/W4224440731","https://openalex.org/W4384161815","https://openalex.org/W2962874517","https://openalex.org/W3094011565"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-08T00:00:00"}