{"id":"https://openalex.org/W2035013249","doi":"https://doi.org/10.1142/s0218127414500357","title":"Limit Cycles of Perturbed Cubic Isochronous Center via the Second Order Averaging Method","display_name":"Limit Cycles of Perturbed Cubic Isochronous Center via the Second Order Averaging Method","publication_year":2014,"publication_date":"2014-03-01","ids":{"openalex":"https://openalex.org/W2035013249","doi":"https://doi.org/10.1142/s0218127414500357","mag":"2035013249"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127414500357","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500357","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/A5100622914","display_name":"Shimin Li","orcid":null},"institutions":[{"id":"https://openalex.org/I201459984","display_name":"Guangdong University Of Finances and Economics","ror":"https://ror.org/0459pv085","country_code":"CN","type":"education","lineage":["https://openalex.org/I201459984"]},{"id":"https://openalex.org/I4210149618","display_name":"Guangdong University of Finance","ror":"https://ror.org/04grzdh47","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210149618"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shimin Li","raw_affiliation_strings":["School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320, P. R. China","institution_ids":["https://openalex.org/I201459984","https://openalex.org/I4210149618"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101834950","display_name":"Yulin Zhao","orcid":"https://orcid.org/0000-0002-4179-2409"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yulin Zhao","raw_affiliation_strings":["Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China","institution_ids":["https://openalex.org/I157773358"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.446,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.62308884,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"24","issue":"03","first_page":"1450035","last_page":"1450035"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/annulus","display_name":"Annulus (botany)","score":0.7747045755386353},{"id":"https://openalex.org/keywords/cubic-function","display_name":"Cubic function","score":0.7328043580055237},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6850925087928772},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6727695465087891},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5630366206169128},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5523338317871094},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.5076161623001099},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4804353415966034},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44154343008995056},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.42345499992370605},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.057424187660217285}],"concepts":[{"id":"https://openalex.org/C150936888","wikidata":"https://www.wikidata.org/wiki/Q4769748","display_name":"Annulus (botany)","level":2,"score":0.7747045755386353},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.7328043580055237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6850925087928772},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6727695465087891},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5630366206169128},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5523338317871094},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.5076161623001099},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4804353415966034},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44154343008995056},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42345499992370605},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.057424187660217285},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127414500357","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500357","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":12,"referenced_works":["https://openalex.org/W1481616730","https://openalex.org/W1556059214","https://openalex.org/W1966709319","https://openalex.org/W1967480646","https://openalex.org/W2020278866","https://openalex.org/W2049815318","https://openalex.org/W2055287145","https://openalex.org/W2070705056","https://openalex.org/W2158334808","https://openalex.org/W2463896629","https://openalex.org/W3041070869","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2379021478","https://openalex.org/W2038876018","https://openalex.org/W2962856853","https://openalex.org/W2015959856","https://openalex.org/W2062758001","https://openalex.org/W3006542548","https://openalex.org/W2388787585","https://openalex.org/W2385987334","https://openalex.org/W2581002549","https://openalex.org/W2060978324"],"abstract_inverted_index":{"In":[0],"this":[1,36,54],"paper,":[2],"we":[3],"bound":[4,55],"the":[5,19,29,50],"number":[6],"of":[7,13,21,32],"limit":[8,45],"cycles":[9,46],"for":[10],"a":[11],"class":[12,20],"cubic":[14,23],"reversible":[15],"isochronous":[16],"system":[17],"inside":[18],"all":[22],"polynomial":[24],"differential":[25],"systems.":[26],"By":[27],"applying":[28],"averaging":[30],"method":[31],"second":[33],"order":[34],"to":[35],"system,":[37],"it":[38],"is":[39,56],"proved":[40],"that":[41],"at":[42],"most":[43],"eight":[44],"can":[47],"bifurcate":[48],"from":[49],"period":[51],"annulus.":[52],"Moreover,":[53],"sharp.":[57]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}