{"id":"https://openalex.org/W2908888005","doi":"https://doi.org/10.1142/s0218127418501754","title":"On the Number of Limit Cycles of Discontinuous Li\u00e9nard Polynomial Differential Systems","display_name":"On the Number of Limit Cycles of Discontinuous Li\u00e9nard Polynomial Differential Systems","publication_year":2018,"publication_date":"2018-12-30","ids":{"openalex":"https://openalex.org/W2908888005","doi":"https://doi.org/10.1142/s0218127418501754","mag":"2908888005"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127418501754","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127418501754","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/A5087741177","display_name":"Fangfang Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fangfang Jiang","raw_affiliation_strings":["School of Science, Jiangnan University, Wuxi 214122, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Science, Jiangnan University, Wuxi 214122, P. R. China","institution_ids":["https://openalex.org/I111599522"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091802290","display_name":"Zhicheng Ji","orcid":"https://orcid.org/0000-0002-4837-7240"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhicheng Ji","raw_affiliation_strings":["School of IoT Engineering, Jiangnan University, Wuxi 214122, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of IoT Engineering, Jiangnan University, Wuxi 214122, P. R. China","institution_ids":["https://openalex.org/I111599522"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100322735","display_name":"Yan Wang","orcid":"https://orcid.org/0000-0002-6026-664X"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yan Wang","raw_affiliation_strings":["School of IoT Engineering, Jiangnan University, Wuxi 214122, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of IoT Engineering, Jiangnan University, Wuxi 214122, P. R. China","institution_ids":["https://openalex.org/I111599522"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100322735"],"corresponding_institution_ids":["https://openalex.org/I111599522"],"apc_list":null,"apc_paid":null,"fwci":0.7588,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.70866022,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":95},"biblio":{"volume":"28","issue":"14","first_page":"1850175","last_page":"1850175"},"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":0.9998999834060669,"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":0.9998999834060669,"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/mathematics","display_name":"Mathematics","score":0.8278340101242065},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.776494026184082},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6281499266624451},{"id":"https://openalex.org/keywords/li\u00e9nard-equation","display_name":"Li\u00e9nard equation","score":0.6209341287612915},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5557531118392944},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5197265148162842},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5179520845413208},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4828975200653076},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46500927209854126},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3729250431060791},{"id":"https://openalex.org/keywords/linear-differential-equation","display_name":"Linear differential equation","score":0.22279277443885803},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11539098620414734},{"id":"https://openalex.org/keywords/exact-differential-equation","display_name":"Exact differential equation","score":0.0770474374294281}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8278340101242065},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.776494026184082},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6281499266624451},{"id":"https://openalex.org/C181154966","wikidata":"https://www.wikidata.org/wiki/Q2500406","display_name":"Li\u00e9nard equation","level":5,"score":0.6209341287612915},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5557531118392944},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5197265148162842},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5179520845413208},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4828975200653076},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46500927209854126},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3729250431060791},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.22279277443885803},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11539098620414734},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.0770474374294281},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127418501754","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127418501754","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":[{"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/W1579026724","https://openalex.org/W1982695814","https://openalex.org/W2001672492","https://openalex.org/W2006732470","https://openalex.org/W2013501206","https://openalex.org/W2014893614","https://openalex.org/W2019143828","https://openalex.org/W2048408728","https://openalex.org/W2054652000","https://openalex.org/W2056447802","https://openalex.org/W2062195828","https://openalex.org/W2067119535","https://openalex.org/W2158334808","https://openalex.org/W2217377229","https://openalex.org/W2493008392","https://openalex.org/W2744176216","https://openalex.org/W2770737626","https://openalex.org/W2913687615","https://openalex.org/W3102220905"],"related_works":["https://openalex.org/W3105025456","https://openalex.org/W3195693990","https://openalex.org/W1967680978","https://openalex.org/W4254482063","https://openalex.org/W3036104585","https://openalex.org/W2996059826","https://openalex.org/W2081519569","https://openalex.org/W2381413956","https://openalex.org/W2478724108","https://openalex.org/W3210315614"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,29],"investigate":[4],"the":[5,21,34,39,49,63],"number":[6,41],"of":[7,13,25,42,53],"limit":[8,43,60],"cycles":[9,61],"for":[10,38],"two":[11],"classes":[12],"discontinuous":[14,26,54],"Li\u00e9nard":[15],"polynomial":[16],"perturbed":[17],"differential":[18,27,55],"systems.":[19],"By":[20],"second-order":[22,50],"averaging":[23,51],"theorem":[24,52],"equations,":[28],"provide":[30],"several":[31],"criteria":[32],"on":[33],"lower":[35],"upper":[36],"bounds":[37],"maximum":[40],"cycles.":[44],"The":[45],"results":[46],"show":[47],"that":[48],"equations":[56],"can":[57],"predict":[58],"more":[59],"than":[62],"first-order":[64],"one.":[65]},"counts_by_year":[{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
