{"id":"https://openalex.org/W2523083646","doi":"https://doi.org/10.1142/s0218127416501716","title":"Limit Cycles for a Class of Piecewise Smooth Quadratic Differential Systems with Multiple Parameters","display_name":"Limit Cycles for a Class of Piecewise Smooth Quadratic Differential Systems with Multiple Parameters","publication_year":2016,"publication_date":"2016-09-01","ids":{"openalex":"https://openalex.org/W2523083646","doi":"https://doi.org/10.1142/s0218127416501716","mag":"2523083646"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416501716","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501716","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/A5022294217","display_name":"Xuekang Bo","orcid":null},"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":"Xuekang Bo","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017250935","display_name":"Yun Tian","orcid":"https://orcid.org/0000-0002-3557-4384"},"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":"Yun Tian","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China","institution_ids":["https://openalex.org/I21945476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I21945476"],"apc_list":null,"apc_paid":null,"fwci":0.5204,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68622108,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"26","issue":"10","first_page":"1650171","last_page":"1650171"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9607999920845032,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9406999945640564,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.8052554130554199},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7805414199829102},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6719517111778259},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6609443426132202},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6566380262374878},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6361864805221558},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5630640387535095},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.4859696626663208},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4854748547077179},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.4614812731742859},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4570044279098511},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.43253055214881897},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39527207612991333},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1369917094707489},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11983466148376465},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07442966103553772}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8052554130554199},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7805414199829102},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6719517111778259},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6609443426132202},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6566380262374878},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6361864805221558},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5630640387535095},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4859696626663208},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4854748547077179},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.4614812731742859},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4570044279098511},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.43253055214881897},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39527207612991333},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1369917094707489},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11983466148376465},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07442966103553772},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416501716","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501716","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":[{"id":"https://openalex.org/G7742653222","display_name":null,"funder_award_id":"11501370","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1552277675","https://openalex.org/W1593811304","https://openalex.org/W1960050943","https://openalex.org/W1986274266","https://openalex.org/W2001672492","https://openalex.org/W2012188622","https://openalex.org/W2014893614","https://openalex.org/W2019766038","https://openalex.org/W2034303126","https://openalex.org/W2042192623","https://openalex.org/W2046380677","https://openalex.org/W2053658423","https://openalex.org/W2068780796","https://openalex.org/W2083933571","https://openalex.org/W2092046534","https://openalex.org/W2256741378","https://openalex.org/W2951830236","https://openalex.org/W3102220905","https://openalex.org/W3105025456"],"related_works":["https://openalex.org/W2765944944","https://openalex.org/W4226164715","https://openalex.org/W2115284473","https://openalex.org/W4327639758","https://openalex.org/W2243882821","https://openalex.org/W1998082046","https://openalex.org/W2154304710","https://openalex.org/W2019676381","https://openalex.org/W1982149897","https://openalex.org/W2387468633"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"a":[3],"class":[4],"of":[5,44],"quadratic":[6],"differential":[7],"systems":[8],"with":[9],"an":[10,50],"isochronous":[11,51],"center":[12],"under":[13],"small":[14],"piecewise":[15],"smooth":[16],"perturbations.":[17],"Two":[18],"perturbation":[19],"parameters":[20],"at":[21],"different":[22],"scales":[23],"are":[24],"included":[25],"in":[26],"the":[27,31,42],"system.":[28],"By":[29],"using":[30],"first":[32],"order":[33],"Melnikov":[34],"function,":[35],"we":[36],"obtain":[37],"some":[38],"new":[39],"results":[40],"on":[41],"number":[43],"small-amplitude":[45],"limit":[46],"cycles":[47],"bifurcating":[48],"around":[49],"center.":[52]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}