{"id":"https://openalex.org/W7118171349","doi":"https://doi.org/10.1142/s0218127426300120","title":"Analysis of Steady-State Solutions and Bifurcations in Higher-Dimensional Piecewise-Linear Systems","display_name":"Analysis of Steady-State Solutions and Bifurcations in Higher-Dimensional Piecewise-Linear Systems","publication_year":2026,"publication_date":"2026-01-03","ids":{"openalex":"https://openalex.org/W7118171349","doi":"https://doi.org/10.1142/s0218127426300120"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127426300120","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127426300120","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/A5121920989","display_name":"Ran Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ran Sun","raw_affiliation_strings":["Interdisciplinary Research Institute, School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, P. R. China"],"raw_orcid":"https://orcid.org/0009-0009-9017-9393","affiliations":[{"raw_affiliation_string":"Interdisciplinary Research Institute, School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, P. R. China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047717019","display_name":"J. Li","orcid":null},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Li","raw_affiliation_strings":["Interdisciplinary Research Institute, School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-7278-2764","affiliations":[{"raw_affiliation_string":"Interdisciplinary Research Institute, School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, P. R. China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051589309","display_name":"Shaotao Zhu","orcid":"https://orcid.org/0000-0002-5670-8986"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shaotao Zhu","raw_affiliation_strings":["College of Computer Science, Beijing University of Technology, Beijing 100124, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-5670-8986","affiliations":[{"raw_affiliation_string":"College of Computer Science, Beijing University of Technology, Beijing 100124, P. R. China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":null,"display_name":"Xinxing Zhou","orcid":"https://orcid.org/0009-0007-0697-9466"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinxing Zhou","raw_affiliation_strings":["Department of Mechanics, Beijing University of Technology, Beijing 100124, P. R. China"],"raw_orcid":"https://orcid.org/0009-0007-0697-9466","affiliations":[{"raw_affiliation_string":"Department of Mechanics, Beijing University of Technology, Beijing 100124, P. R. China","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I37796252"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01402239,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":"05","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12435","display_name":"Bladed Disk Vibration Dynamics","score":0.6079000234603882,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12435","display_name":"Bladed Disk Vibration Dynamics","score":0.6079000234603882,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.08449999988079071,"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/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.06800000369548798,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7005000114440918},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.6254000067710876},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4796000123023987},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4569000005722046},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.4163999855518341},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.387800008058548},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.3806999921798706},{"id":"https://openalex.org/keywords/subharmonic-function","display_name":"Subharmonic function","score":0.37880000472068787},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.36880001425743103}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7005000114440918},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6736999750137329},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.6254000067710876},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5504999756813049},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4796000123023987},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4569000005722046},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.4163999855518341},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3806999921798706},{"id":"https://openalex.org/C29373527","wikidata":"https://www.wikidata.org/wiki/Q753658","display_name":"Subharmonic function","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.36880001425743103},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.36809998750686646},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.32739999890327454},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.2992999851703644},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2969000041484833},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.28519999980926514},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.28369998931884766},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.26429998874664307},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2515999972820282},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.2508000135421753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127426300120","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127426300120","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":[{"id":"https://openalex.org/G342522193","display_name":null,"funder_award_id":"12272011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4504684578","display_name":null,"funder_award_id":"2022YFB3806000","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G544570890","display_name":null,"funder_award_id":"12332001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W45508539","https://openalex.org/W223797242","https://openalex.org/W610924978","https://openalex.org/W1981602625","https://openalex.org/W1987960945","https://openalex.org/W2007785017","https://openalex.org/W2025364658","https://openalex.org/W2033225924","https://openalex.org/W2033345573","https://openalex.org/W2038062847","https://openalex.org/W2051822743","https://openalex.org/W2059074408","https://openalex.org/W2066639428","https://openalex.org/W2067378651","https://openalex.org/W2069362455","https://openalex.org/W2077913859","https://openalex.org/W2080360523","https://openalex.org/W2090573856","https://openalex.org/W2119764378","https://openalex.org/W2226829440","https://openalex.org/W2275890290","https://openalex.org/W2304174616","https://openalex.org/W2498396418","https://openalex.org/W2600037820","https://openalex.org/W2606613617","https://openalex.org/W2791824395","https://openalex.org/W3006098754","https://openalex.org/W3006143744","https://openalex.org/W3024831282","https://openalex.org/W3033580677","https://openalex.org/W3047839770","https://openalex.org/W3081446155","https://openalex.org/W3119009781","https://openalex.org/W4220986557","https://openalex.org/W4221022313","https://openalex.org/W4287577667","https://openalex.org/W4297178704","https://openalex.org/W4298007055","https://openalex.org/W4307892346","https://openalex.org/W4308750499","https://openalex.org/W4322505743","https://openalex.org/W4378895239","https://openalex.org/W4393352598","https://openalex.org/W4396573946","https://openalex.org/W4406473998","https://openalex.org/W4406475335","https://openalex.org/W4412695297"],"related_works":[],"abstract_inverted_index":{"Vibration":[0],"systems":[1],"with":[2],"multiple":[3],"potential":[4],"wells":[5],"can":[6],"often":[7],"be":[8],"approximated":[9],"by":[10,99,118],"higher-dimensional":[11,49],"piecewise-linear":[12,50,66,92],"nonsmooth":[13],"systems,":[14,35],"whose":[15],"responses":[16,32,134],"typically":[17],"consist":[18],"of":[19,33,47,59,90,106,135],"complex":[20],"frequency":[21,157],"components.":[22],"Existing":[23],"studies":[24],"provide":[25],"limited":[26],"analytical":[27,114],"insights":[28],"into":[29,96],"the":[30,38,44,76,91,104,122,132,136],"steady-state":[31],"such":[34],"incompletely":[36],"revealing":[37],"response":[39],"characteristics.":[40],"This":[41],"work":[42],"investigates":[43],"bifurcation":[45,143,152],"behavior":[46,144],"a":[48,60,65,81],"system":[51,57,93,137],"subjected":[52],"to":[53,74,130],"low-frequency":[54,139],"excitation.":[55,141],"The":[56,69,87,142],"consists":[58],"coupled":[61],"linear":[62],"oscillator":[63],"and":[64,159],"quadruple-well":[67],"structure.":[68],"Euler\u2013Lagrange":[70],"equation":[71],"is":[72,85,94,116,145],"employed":[73],"establish":[75],"dynamic":[77],"model,":[78],"from":[79],"which":[80,103],"corresponding":[82],"dimensionless":[83],"form":[84],"derived.":[86],"phase":[88,148],"space":[89],"divided":[95],"seven":[97],"regions":[98],"switching":[100,123],"manifolds,":[101],"within":[102],"equations":[105],"motion":[107],"are":[108,127],"linear.":[109],"On":[110],"this":[111],"basis,":[112],"an":[113],"method":[115],"developed":[117],"constructing":[119],"mappings":[120],"across":[121],"manifolds.":[124],"Numerical":[125],"simulations":[126],"then":[128],"performed":[129],"examine":[131],"superharmonic":[133],"under":[138],"sinusoidal":[140],"analyzed":[146],"using":[147],"portraits,":[149],"time":[150],"histories,":[151],"diagrams,":[153],"power":[154],"spectral":[155],"density,":[156],"spectra,":[158],"Lyapunov":[160],"exponent":[161],"spectra.":[162]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-01-05T00:00:00"}
