{"id":"https://openalex.org/W4414912985","doi":"https://doi.org/10.1007/s00332-025-10216-w","title":"Bifurcations of Tangent Points and Critical Loops in Piecewise-Smooth Systems","display_name":"Bifurcations of Tangent Points and Critical Loops in Piecewise-Smooth Systems","publication_year":2025,"publication_date":"2025-10-07","ids":{"openalex":"https://openalex.org/W4414912985","doi":"https://doi.org/10.1007/s00332-025-10216-w"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-025-10216-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-025-10216-w","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","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/A5007700786","display_name":"Zhihao Fang","orcid":"https://orcid.org/0000-0002-5980-4244"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhihao Fang","raw_affiliation_strings":["School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, P. R. China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025509123","display_name":"Xingwu Chen","orcid":"https://orcid.org/0000-0002-1450-0503"},"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":"Xingwu Chen","raw_affiliation_strings":["School of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, P. R. China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007700786"],"corresponding_institution_ids":["https://openalex.org/I25757504"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.34306395,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"6","first_page":null,"last_page":null},"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":0.9800000190734863,"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/T10244","display_name":"Chaos control and synchronization","score":0.9695000052452087,"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/degeneracy","display_name":"Degeneracy (biology)","score":0.8403000235557556},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.6500999927520752},{"id":"https://openalex.org/keywords/tangent-vector","display_name":"Tangent vector","score":0.6269000172615051},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5472999811172485},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5461000204086304},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5163000226020813},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.460999995470047},{"id":"https://openalex.org/keywords/critical-point","display_name":"Critical point (mathematics)","score":0.4609000086784363},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.43290001153945923}],"concepts":[{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.8403000235557556},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.6500999927520752},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.6269000172615051},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6096000075340271},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5472999811172485},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5461000204086304},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5289999842643738},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5163000226020813},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.460999995470047},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.4609000086784363},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.43290001153945923},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.4203999936580658},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41589999198913574},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3598000109195709},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.32710000872612},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.32269999384880066},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.3043000102043152},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2563000023365021}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00332-025-10216-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-025-10216-w","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","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":38,"referenced_works":["https://openalex.org/W49800840","https://openalex.org/W1269033259","https://openalex.org/W1514578360","https://openalex.org/W1552277675","https://openalex.org/W1557324374","https://openalex.org/W1593811304","https://openalex.org/W1596321532","https://openalex.org/W1603340857","https://openalex.org/W1974272814","https://openalex.org/W1980228211","https://openalex.org/W2007232274","https://openalex.org/W2047449028","https://openalex.org/W2053658423","https://openalex.org/W2064246405","https://openalex.org/W2072652000","https://openalex.org/W2079569562","https://openalex.org/W2083823140","https://openalex.org/W2089466166","https://openalex.org/W2092046534","https://openalex.org/W2105169467","https://openalex.org/W2125594969","https://openalex.org/W2133505353","https://openalex.org/W2778531943","https://openalex.org/W2888212697","https://openalex.org/W2888615804","https://openalex.org/W2955319508","https://openalex.org/W2963528677","https://openalex.org/W3089267081","https://openalex.org/W3164731291","https://openalex.org/W3169457090","https://openalex.org/W3208535967","https://openalex.org/W3210756239","https://openalex.org/W4214769085","https://openalex.org/W4220957425","https://openalex.org/W4223494807","https://openalex.org/W4229035536","https://openalex.org/W4293078920","https://openalex.org/W4383045267"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}