{"id":"https://openalex.org/W186891","doi":"https://doi.org/10.1007/bfb0085395","title":"Conditions for a centre and the bifurcation of limit cycles in a class of cubic systems","display_name":"Conditions for a centre and the bifurcation of limit cycles in a class of cubic systems","publication_year":1990,"publication_date":"1990-01-01","ids":{"openalex":"https://openalex.org/W186891","doi":"https://doi.org/10.1007/bfb0085395","mag":"186891"},"language":"en","primary_location":{"id":"doi:10.1007/bfb0085395","doi":"https://doi.org/10.1007/bfb0085395","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0085395","pdf_url":null,"source":{"id":"https://openalex.org/S118039931","display_name":"Lecture notes in mathematics","issn_l":"0075-8434","issn":["0075-8434","1617-9692"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Mathematics","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W186906267","display_name":"Bifurcations of Planar Vector Fields"},"type":"book-chapter","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/A5111498049","display_name":"NG Lloyd","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I16038530","display_name":"Aberystwyth University","ror":"https://ror.org/015m2p889","country_code":"GB","type":"education","lineage":["https://openalex.org/I16038530"]},{"id":"https://openalex.org/I97429440","display_name":"University of Wales","ror":"https://ror.org/01se4f844","country_code":"GB","type":"education","lineage":["https://openalex.org/I97429440"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"NG Lloyd","raw_affiliation_strings":["Department of Mathematics, The University College of Wales, Aberystwyth, UK","The University College of Wales"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University College of Wales, Aberystwyth, UK","institution_ids":["https://openalex.org/I16038530"]},{"raw_affiliation_string":"The University College of Wales","institution_ids":["https://openalex.org/I16038530","https://openalex.org/I97429440"]}]},{"author_position":"last","author":{"id":null,"display_name":"JM Pearson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I16038530","display_name":"Aberystwyth University","ror":"https://ror.org/015m2p889","country_code":"GB","type":"education","lineage":["https://openalex.org/I16038530"]},{"id":"https://openalex.org/I97429440","display_name":"University of Wales","ror":"https://ror.org/01se4f844","country_code":"GB","type":"education","lineage":["https://openalex.org/I97429440"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"JM Pearson","raw_affiliation_strings":["Department of Mathematics, The University College of Wales, Aberystwyth, UK","The University College of Wales"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University College of Wales, Aberystwyth, UK","institution_ids":["https://openalex.org/I16038530"]},{"raw_affiliation_string":"The University College of Wales","institution_ids":["https://openalex.org/I16038530","https://openalex.org/I97429440"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9046,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.92300725,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"230","last_page":"242"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.0,"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/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/limit-cycles","display_name":"limit cycles","score":0.6690000295639038},{"id":"https://openalex.org/keywords/bifurcation-of-limit-cycles","display_name":"bifurcation of limit cycles","score":0.8970000147819519},{"id":"https://openalex.org/keywords/cubic-systems","display_name":"cubic systems","score":0.8199999928474426},{"id":"https://openalex.org/keywords/center-conditions","display_name":"center conditions","score":0.6370000243186951},{"id":"https://openalex.org/keywords/planar-polynomial-differential-systems","display_name":"planar polynomial differential systems","score":0.6110000014305115},{"id":"https://openalex.org/keywords/center-focus-problem","display_name":"center-focus problem","score":0.39500001072883606}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8411147594451904},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6850544214248657},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.604899525642395},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5821129083633423},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.4461110532283783},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41686341166496277},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15039706230163574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06363749504089355},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0596640408039093},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.03909105062484741},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bfb0085395","doi":"https://doi.org/10.1007/bfb0085395","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0085395","pdf_url":null,"source":{"id":"https://openalex.org/S118039931","display_name":"Lecture notes in mathematics","issn_l":"0075-8434","issn":["0075-8434","1617-9692"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Mathematics","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.5099999904632568,"id":"https://metadata.un.org/sdg/13","display_name":"Climate action"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1546156674","https://openalex.org/W2001783958","https://openalex.org/W2027868522","https://openalex.org/W2046858619","https://openalex.org/W2061361830","https://openalex.org/W2072011217","https://openalex.org/W2073841414","https://openalex.org/W2118604725","https://openalex.org/W2124141913","https://openalex.org/W2129875234","https://openalex.org/W2990394733"],"related_works":["https://openalex.org/W2051439117","https://openalex.org/W4388297534","https://openalex.org/W1673883441","https://openalex.org/W3195693990","https://openalex.org/W4298109871","https://openalex.org/W2313188567","https://openalex.org/W4248124207","https://openalex.org/W2996059826","https://openalex.org/W2083477739","https://openalex.org/W2087320822"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}