{"id":"https://openalex.org/W2522606122","doi":"https://doi.org/10.1142/s0218127416501686","title":"On the Number of Limit Cycles by Perturbing a Piecewise Smooth Li\u00e9nard Model","display_name":"On the Number of Limit Cycles by Perturbing a Piecewise Smooth Li\u00e9nard Model","publication_year":2016,"publication_date":"2016-09-01","ids":{"openalex":"https://openalex.org/W2522606122","doi":"https://doi.org/10.1142/s0218127416501686","mag":"2522606122"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416501686","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501686","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/A5089991046","display_name":"Lijuan Sheng","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":"Lijuan Sheng","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030649439","display_name":"Maoan Han","orcid":"https://orcid.org/0000-0001-8792-1256"},"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":true,"raw_author_name":"Maoan Han","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"],"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/A5074639752","display_name":"Valery Romanovsky","orcid":null},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Valery Romanovsky","raw_affiliation_strings":["Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000, Slovenia","Faculty of Natural Science and Mathematics, University of Maribor, Koro\u0161ka Cesta 160, SI-2000 Maribor, Slovenia"],"affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Faculty of Natural Science and Mathematics, University of Maribor, Koro\u0161ka Cesta 160, SI-2000 Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030649439"],"corresponding_institution_ids":["https://openalex.org/I21945476"],"apc_list":null,"apc_paid":null,"fwci":0.571,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70708814,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"26","issue":"10","first_page":"1650168","last_page":"1650168"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.988099992275238,"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"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9868000149726868,"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/mathematics","display_name":"Mathematics","score":0.7669645547866821},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.7633928060531616},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7387582063674927},{"id":"https://openalex.org/keywords/annulus","display_name":"Annulus (botany)","score":0.7214592695236206},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6270140409469604},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.5789443254470825},{"id":"https://openalex.org/keywords/li\u00e9nard-equation","display_name":"Li\u00e9nard equation","score":0.5562564730644226},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5237362384796143},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5195468068122864},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4958265721797943},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3754144012928009},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.37446293234825134},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.34294000267982483}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7669645547866821},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7633928060531616},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7387582063674927},{"id":"https://openalex.org/C150936888","wikidata":"https://www.wikidata.org/wiki/Q4769748","display_name":"Annulus (botany)","level":2,"score":0.7214592695236206},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6270140409469604},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.5789443254470825},{"id":"https://openalex.org/C181154966","wikidata":"https://www.wikidata.org/wiki/Q2500406","display_name":"Li\u00e9nard equation","level":5,"score":0.5562564730644226},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5237362384796143},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5195468068122864},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4958265721797943},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3754144012928009},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.37446293234825134},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34294000267982483},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416501686","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501686","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":27,"referenced_works":["https://openalex.org/W1548708049","https://openalex.org/W1968629527","https://openalex.org/W1976084307","https://openalex.org/W1982088565","https://openalex.org/W1995373224","https://openalex.org/W2034022724","https://openalex.org/W2034303126","https://openalex.org/W2034444332","https://openalex.org/W2034821539","https://openalex.org/W2040186806","https://openalex.org/W2041526529","https://openalex.org/W2043228698","https://openalex.org/W2046380677","https://openalex.org/W2049544062","https://openalex.org/W2053380598","https://openalex.org/W2067856853","https://openalex.org/W2068780796","https://openalex.org/W2071479141","https://openalex.org/W2081699720","https://openalex.org/W2083933571","https://openalex.org/W2093849459","https://openalex.org/W2111496031","https://openalex.org/W2172025630","https://openalex.org/W2256741378","https://openalex.org/W3105025456","https://openalex.org/W4237970627","https://openalex.org/W4252495814"],"related_works":["https://openalex.org/W4226164715","https://openalex.org/W3096660584","https://openalex.org/W2062758001","https://openalex.org/W2364054655","https://openalex.org/W2745969591","https://openalex.org/W3021048270","https://openalex.org/W2266604143","https://openalex.org/W3105025456","https://openalex.org/W2254730430","https://openalex.org/W2976651471"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,43],"study":[4],"the":[5,29,32,46,57,65],"number":[6,59],"of":[7,40,60],"limit":[8,61],"cycles":[9,62],"by":[10],"perturbing":[11],"a":[12,38],"Li\u00e9nard":[13,34],"model":[14],"[Formula:":[15,18,22],"see":[16,19,23],"text]":[17,24],"text],":[20],"where":[21],"is":[25],"piecewise":[26],"smooth.":[27],"Under":[28],"assumption":[30],"that":[31],"unperturbed":[33],"type":[35],"system":[36],"has":[37],"family":[39],"periodic":[41],"orbits,":[42],"first":[44,50],"deduce":[45],"expression":[47],"for":[48],"its":[49],"order":[51],"Melnikov":[52],"function,":[53],"and":[54],"then":[55],"obtain":[56],"maximum":[58],"bifurcating":[63],"from":[64],"period":[66],"annulus.":[67]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
