{"id":"https://openalex.org/W2046210296","doi":"https://doi.org/10.1142/s0218127414501417","title":"Degenerate Grazing Bifurcations in a Simple Bilinear Oscillator","display_name":"Degenerate Grazing Bifurcations in a Simple Bilinear Oscillator","publication_year":2014,"publication_date":"2014-11-01","ids":{"openalex":"https://openalex.org/W2046210296","doi":"https://doi.org/10.1142/s0218127414501417","mag":"2046210296"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127414501417","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414501417","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/A5100859945","display_name":"Tingting Yi","orcid":null},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tingting Yi","raw_affiliation_strings":["Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China","Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R., China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China","institution_ids":["https://openalex.org/I24185976"]},{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R., China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079719473","display_name":"Zhengdong Du","orcid":"https://orcid.org/0000-0003-3550-0817"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengdong Du","raw_affiliation_strings":["Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China","Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R., China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China","institution_ids":["https://openalex.org/I24185976"]},{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R., China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I24185976"],"apc_list":null,"apc_paid":null,"fwci":0.229,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.55817867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"11","first_page":"1450141","last_page":"1450141"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9965999722480774,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9965999722480774,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9958000183105469,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.7193666696548462},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.608578622341156},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.607633113861084},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4875180423259735},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.4456421434879303},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.44352179765701294},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.42108750343322754},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4148141145706177},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4137928783893585},{"id":"https://openalex.org/keywords/grazing","display_name":"Grazing","score":0.410092830657959},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.3780094087123871},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3031812906265259},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17565223574638367},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16355356574058533}],"concepts":[{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.7193666696548462},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.608578622341156},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.607633113861084},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4875180423259735},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.4456421434879303},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.44352179765701294},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.42108750343322754},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4148141145706177},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4137928783893585},{"id":"https://openalex.org/C2777904157","wikidata":"https://www.wikidata.org/wiki/Q3239189","display_name":"Grazing","level":2,"score":0.410092830657959},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.3780094087123871},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3031812906265259},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17565223574638367},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16355356574058533},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127414501417","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414501417","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W212323982","https://openalex.org/W344044850","https://openalex.org/W635061704","https://openalex.org/W1479681305","https://openalex.org/W1536103813","https://openalex.org/W1552277675","https://openalex.org/W1593811304","https://openalex.org/W1606868977","https://openalex.org/W1803676133","https://openalex.org/W1972735070","https://openalex.org/W1973112162","https://openalex.org/W1973113707","https://openalex.org/W1984838918","https://openalex.org/W1990717556","https://openalex.org/W1994955119","https://openalex.org/W1997313126","https://openalex.org/W2005988040","https://openalex.org/W2011227277","https://openalex.org/W2014534896","https://openalex.org/W2020783811","https://openalex.org/W2030450697","https://openalex.org/W2031604902","https://openalex.org/W2033454068","https://openalex.org/W2039669398","https://openalex.org/W2042192623","https://openalex.org/W2050121967","https://openalex.org/W2059646457","https://openalex.org/W2066639428","https://openalex.org/W2077707516","https://openalex.org/W2078887983","https://openalex.org/W2080798477","https://openalex.org/W2082444786","https://openalex.org/W2083499041","https://openalex.org/W2084092760","https://openalex.org/W2084127152","https://openalex.org/W2099687578","https://openalex.org/W2125161896","https://openalex.org/W2144249884","https://openalex.org/W2146896171","https://openalex.org/W2158682041","https://openalex.org/W2159263027","https://openalex.org/W2164297166","https://openalex.org/W2496842803","https://openalex.org/W3150913747","https://openalex.org/W4293772582","https://openalex.org/W4300220933"],"related_works":["https://openalex.org/W2246258018","https://openalex.org/W2114933532","https://openalex.org/W1981636441","https://openalex.org/W4296238711","https://openalex.org/W1967675726","https://openalex.org/W2084499748","https://openalex.org/W1544214907","https://openalex.org/W4300835405","https://openalex.org/W2402814031","https://openalex.org/W2059546211"],"abstract_inverted_index":{"Degenerate":[0],"grazing":[1,40,57,105],"bifurcation":[2,58],"occurring":[3],"in":[4,47,88,96],"a":[5,30,56,67],"simple":[6],"bilinear":[7],"oscillator,":[8,20],"namely":[9],"the":[10,15,34,42,48,52,62,75],"limit":[11],"discontinuous":[12,18],"case":[13],"of":[14,51,61,100,103],"smooth":[16],"and":[17],"(SD)":[19],"is":[21,91],"investigated":[22],"by":[23],"numerical":[24,71],"simulations.":[25],"The":[26,45,85],"unperturbed":[27],"system":[28],"has":[29,66],"saddle-like":[31],"singularity":[32],"at":[33,41,55],"origin":[35],"with":[36],"two":[37,63],"periodic":[38,64],"orbits":[39,65],"same":[43],"point.":[44],"matrix":[46],"leading-order":[49],"truncation":[50],"Poincar\u00e9":[53],"map":[54],"for":[59],"either":[60],"zero":[68],"eigenvalue.":[69],"Our":[70],"experiments":[72],"suggest":[73],"that":[74],"near-grazing":[76],"dynamics":[77],"are":[78],"much":[79],"more":[80],"complicated":[81],"than":[82],"previously":[83],"found.":[84],"results":[86],"obtained":[87],"this":[89,101],"paper":[90],"expected":[92],"to":[93],"be":[94],"useful":[95],"developing":[97],"analytical":[98],"methods":[99],"type":[102],"degenerate":[104],"bifurcations.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}