{"id":"https://openalex.org/W2345988157","doi":"https://doi.org/10.1142/s0218127416500619","title":"Global Analysis on the Discontinuous Limit Case of a Smooth Oscillator","display_name":"Global Analysis on the Discontinuous Limit Case of a Smooth Oscillator","publication_year":2016,"publication_date":"2016-04-01","ids":{"openalex":"https://openalex.org/W2345988157","doi":"https://doi.org/10.1142/s0218127416500619","mag":"2345988157"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416500619","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500619","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/A5033325860","display_name":"Hebai Chen","orcid":"https://orcid.org/0000-0003-1601-1014"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hebai Chen","raw_affiliation_strings":["School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, P. R. China","institution_ids":["https://openalex.org/I4800084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033325860"],"corresponding_institution_ids":["https://openalex.org/I4800084"],"apc_list":null,"apc_paid":null,"fwci":2.6022,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.88159383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"04","first_page":"1650061","last_page":"1650061"},"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9814000129699707,"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/phase-portrait","display_name":"Phase portrait","score":0.7523860335350037},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.7340891361236572},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7219325304031372},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.7065508365631104},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6954358220100403},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6738716959953308},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6634162068367004},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.6068795919418335},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5669127106666565},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.5452741384506226},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5073515772819519},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4487725794315338},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4152672290802002},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19621875882148743},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16156721115112305},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13495773077011108},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07811012864112854},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06307822465896606}],"concepts":[{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.7523860335350037},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.7340891361236572},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7219325304031372},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.7065508365631104},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6954358220100403},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6738716959953308},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6634162068367004},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.6068795919418335},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5669127106666565},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.5452741384506226},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5073515772819519},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4487725794315338},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4152672290802002},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19621875882148743},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16156721115112305},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13495773077011108},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07811012864112854},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06307822465896606},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416500619","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500619","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"},{"id":"https://openalex.org/F4320322720","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693"},{"id":"https://openalex.org/F4320323711","display_name":"Southwest University","ror":"https://ror.org/01kj4z117"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W147551077","https://openalex.org/W176407471","https://openalex.org/W1515307033","https://openalex.org/W1536103813","https://openalex.org/W1552277675","https://openalex.org/W1592648094","https://openalex.org/W1593811304","https://openalex.org/W2042192623","https://openalex.org/W2047449028","https://openalex.org/W2059646457","https://openalex.org/W2063816603","https://openalex.org/W2066639428","https://openalex.org/W2077707516","https://openalex.org/W2083823140","https://openalex.org/W2084730754","https://openalex.org/W2088827616","https://openalex.org/W2089876099","https://openalex.org/W2091384477","https://openalex.org/W2123042723","https://openalex.org/W2125161896","https://openalex.org/W2164297166","https://openalex.org/W2596027227","https://openalex.org/W2739685101","https://openalex.org/W4293078920","https://openalex.org/W4293772582"],"related_works":["https://openalex.org/W2978842908","https://openalex.org/W2974193234","https://openalex.org/W2923981205","https://openalex.org/W2775656422","https://openalex.org/W2785329944","https://openalex.org/W4205607476","https://openalex.org/W2345988157","https://openalex.org/W3002144095","https://openalex.org/W2923145936","https://openalex.org/W2375987874"],"abstract_inverted_index":{"Global":[0],"dynamics":[1],"of":[2,5,17,33,50,71],"a":[3,13,18,48,83],"class":[4],"planar":[6],"Filippov":[7],"systems":[8],"with":[9],"symmetry,":[10],"which":[11],"is":[12,21,39,57],"discontinuous":[14],"limit":[15,34,45],"case":[16],"smooth":[19],"oscillator,":[20],"studied.":[22],"Necessary":[23],"and":[24,30,65,82],"sufficient":[25],"conditions":[26],"for":[27],"the":[28,31,66,72],"existence":[29],"number":[32],"cycles":[35,46],"are":[36,76,88,94],"given.":[37],"It":[38],"shown":[40],"that":[41],"at":[42],"most":[43],"two":[44],"or":[47],"pair":[49],"grazing":[51,61,73],"loops":[52],"exist.":[53],"A":[54],"special":[55],"method":[56],"introduced":[58],"to":[59],"study":[60],"bifurcation.":[62],"The":[63],"monotonicity":[64],"[Formula:":[67],"see":[68],"text]":[69],"smoothness":[70],"bifurcation":[74,86],"curve":[75],"proved.":[77],"All":[78],"global":[79,85],"phase":[80],"portraits":[81],"complete":[84],"diagram":[87],"described.":[89],"Finally,":[90],"some":[91],"numerical":[92],"examples":[93],"demonstrated.":[95]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
