{"id":"https://openalex.org/W2596496843","doi":"https://doi.org/10.1137/17m1110584","title":"Generalized Play Hysteresis Operators in Limits of Fast-Slow Systems","display_name":"Generalized Play Hysteresis Operators in Limits of Fast-Slow Systems","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2596496843","doi":"https://doi.org/10.1137/17m1110584","mag":"2596496843"},"language":"en","primary_location":{"id":"doi:10.1137/17m1110584","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1110584","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1701.00229","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Christian Kuehn","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christian Kuehn","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Christian M\u00fcnch","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian M\u00fcnch","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.427,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.82136904,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"16","issue":"3","first_page":"1650","last_page":"1685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11525","display_name":"Piezoelectric Actuators and Control","score":0.8880000114440918,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11525","display_name":"Piezoelectric Actuators and Control","score":0.8880000114440918,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.008899999782443047,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11486","display_name":"Micro and Nano Robotics","score":0.007499999832361937,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6017000079154968},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5771999955177307},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5340999960899353},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5307000279426575},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5020999908447266},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.4959999918937683},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.43810001015663147},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.43529999256134033},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4212000072002411}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.701200008392334},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6017000079154968},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5771999955177307},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5340999960899353},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5307000279426575},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5020999908447266},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.4959999918937683},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.43810001015663147},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.43529999256134033},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4212000072002411},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.38850000500679016},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38659998774528503},{"id":"https://openalex.org/C123299182","wikidata":"https://www.wikidata.org/wiki/Q190837","display_name":"Hysteresis","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3650999963283539},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.34540000557899475},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.3450999855995178},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.326200008392334},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.3156000077724457},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3091999888420105},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.2578999996185303}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1110584","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1110584","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1701.00229","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.00229","pdf_url":"https://arxiv.org/pdf/1701.00229","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1701.00229","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.00229","pdf_url":"https://arxiv.org/pdf/1701.00229","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8468999685","display_name":null,"funder_award_id":"IGDK 1754","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320882","display_name":"Volkswagen Foundation","ror":"https://ror.org/03bsmfz84"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W99189181","https://openalex.org/W140547310","https://openalex.org/W1484182740","https://openalex.org/W1658792376","https://openalex.org/W1688235387","https://openalex.org/W1968435495","https://openalex.org/W1970878334","https://openalex.org/W1981961598","https://openalex.org/W1983924943","https://openalex.org/W1987576052","https://openalex.org/W1989046305","https://openalex.org/W2000871268","https://openalex.org/W2007873130","https://openalex.org/W2016767879","https://openalex.org/W2018888755","https://openalex.org/W2027728683","https://openalex.org/W2028385516","https://openalex.org/W2030625405","https://openalex.org/W2053205765","https://openalex.org/W2070555670","https://openalex.org/W2070595246","https://openalex.org/W2072411062","https://openalex.org/W2074969451","https://openalex.org/W2090709920","https://openalex.org/W2093823001","https://openalex.org/W2100378730","https://openalex.org/W2101697338","https://openalex.org/W2101714536","https://openalex.org/W2145281112","https://openalex.org/W2145894459","https://openalex.org/W2146073476","https://openalex.org/W2150823207","https://openalex.org/W2315938601","https://openalex.org/W2320358449","https://openalex.org/W2418151482"],"related_works":[],"abstract_inverted_index":{"Hysteresis":[0],"operators":[1,37,58,101],"appear":[2],"in":[3,59,102,129,148,159,164,188],"many":[4],"applications,":[5],"such":[6],"as":[7,62],"elasto-plasticity":[8],"and":[9,11,142],"micromagnetics,":[10],"can":[12,182],"be":[13],"used":[14,44],"for":[15,30,184],"a":[16,25,63,78,91,136],"wider":[17],"class":[18],"of":[19,32,65,80,86,110,119,156,162,172],"systems,":[20,41],"where":[21],"rate-independent":[22],"memory":[23,50],"plays":[24],"role.":[26],"A":[27],"natural":[28],"approximation":[29,45],"systems":[31,89,117],"evolution":[33],"equations":[34,55],"with":[35,56,90],"hysteresis":[36,57],"are":[38,95],"fast-slow":[39,67,88,116,168],"dynamical":[40],"which---in":[42],"their":[43],"form---do":[46],"not":[47],"involve":[48],"any":[49],"effects.":[51],"Hence,":[52],"viewing":[53],"differential":[54],"the":[60,103,115,133,160],"nonlinearity":[61],"limit":[64,71],"approximating":[66],"dynamics":[68],"involves":[69],"subtle":[70],"procedures.":[72],"In":[73],"this":[74,111,173],"paper,":[75],"we":[76],"give":[77],"proof":[79,124],"Netushil's":[81],"\u201cobservation\u201d":[82,112],"that":[83,178],"broad":[84],"classes":[85],"planar":[87,166,189],"two-dimensional":[92,185],"critical":[93,186],"manifold":[94],"expected":[96],"to":[97],"yield":[98],"generalized":[99],"play":[100],"singular":[104],"limit.":[105],"We":[106,151],"provide":[107,153],"two":[108],"proofs":[109],"based":[113],"upon":[114],"paradigm":[118],"decomposition":[120],"into":[121],"subsystems.":[122],"One":[123],"strategy":[125,138],"employs":[126],"suitable":[127],"convergence":[128],"function":[130],"spaces,":[131],"while":[132],"other":[134],"considers":[135],"geometric":[137],"via":[139],"local":[140],"linearization":[141],"patching":[143],"adapted":[144],"originally":[145],"from":[146],"problems":[147],"stochastic":[149],"analysis.":[150],"also":[152,175],"an":[154],"illustration":[155],"our":[157],"results":[158],"context":[161],"oscillations":[163],"forced":[165],"nonautonomous":[167],"systems.":[169,190],"The":[170],"study":[171],"example":[174],"strongly":[176],"suggests":[177],"new":[179],"canard-type":[180],"mechanisms":[181],"occur":[183],"manifolds":[187]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2017-03-23T00:00:00"}