{"id":"https://openalex.org/W1204777979","doi":"https://doi.org/10.1137/140965818","title":"Canards of Folded Saddle-Node Type I","display_name":"Canards of Folded Saddle-Node Type I","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1204777979","doi":"https://doi.org/10.1137/140965818","mag":"1204777979"},"language":"en","primary_location":{"id":"doi:10.1137/140965818","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140965818","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5072290038","display_name":"Theodore Vo","orcid":"https://orcid.org/0000-0003-4243-0044"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Theodore Vo","raw_affiliation_strings":["Boston University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Boston University","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089288259","display_name":"Martin Wechselberger","orcid":"https://orcid.org/0000-0003-2681-3440"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Martin Wechselberger","raw_affiliation_strings":["University of Sydney"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Sydney","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2475,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.91536317,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"47","issue":"4","first_page":"3235","last_page":"3283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9997000098228455,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9997000098228455,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9921000003814697,"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/mathematics","display_name":"Mathematics","score":0.739957332611084},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6544344425201416},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5792230367660522},{"id":"https://openalex.org/keywords/van-der-pol-oscillator","display_name":"Van der Pol oscillator","score":0.5663635730743408},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.5480251312255859},{"id":"https://openalex.org/keywords/slow-manifold","display_name":"Slow manifold","score":0.5395938158035278},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5097557902336121},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.4998800754547119},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.4612935781478882},{"id":"https://openalex.org/keywords/codimension","display_name":"Codimension","score":0.4555940628051758},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4336966276168823},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.42916280031204224},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.4168388247489929},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.29529818892478943},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20113354921340942},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13615265488624573}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.739957332611084},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6544344425201416},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5792230367660522},{"id":"https://openalex.org/C98010927","wikidata":"https://www.wikidata.org/wiki/Q2081515","display_name":"Van der Pol oscillator","level":3,"score":0.5663635730743408},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.5480251312255859},{"id":"https://openalex.org/C2778671503","wikidata":"https://www.wikidata.org/wiki/Q7542110","display_name":"Slow manifold","level":3,"score":0.5395938158035278},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5097557902336121},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.4998800754547119},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.4612935781478882},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.4555940628051758},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4336966276168823},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.42916280031204224},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.4168388247489929},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29529818892478943},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20113354921340942},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13615265488624573},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140965818","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140965818","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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":43,"referenced_works":["https://openalex.org/W1484182740","https://openalex.org/W1965157995","https://openalex.org/W1965780186","https://openalex.org/W1967771793","https://openalex.org/W1973909460","https://openalex.org/W1974614991","https://openalex.org/W1981961598","https://openalex.org/W1983924943","https://openalex.org/W1986739294","https://openalex.org/W1987576052","https://openalex.org/W1988934258","https://openalex.org/W1990139416","https://openalex.org/W2002570644","https://openalex.org/W2005046954","https://openalex.org/W2006109372","https://openalex.org/W2008187346","https://openalex.org/W2016766047","https://openalex.org/W2016767879","https://openalex.org/W2018250376","https://openalex.org/W2022543096","https://openalex.org/W2024858188","https://openalex.org/W2026965359","https://openalex.org/W2033540777","https://openalex.org/W2038631673","https://openalex.org/W2041579436","https://openalex.org/W2055748712","https://openalex.org/W2057545369","https://openalex.org/W2063827672","https://openalex.org/W2080018957","https://openalex.org/W2086770172","https://openalex.org/W2088017330","https://openalex.org/W2089995439","https://openalex.org/W2093823001","https://openalex.org/W2094429103","https://openalex.org/W2099882536","https://openalex.org/W2101714536","https://openalex.org/W2113751538","https://openalex.org/W2146926264","https://openalex.org/W2153904027","https://openalex.org/W2169938087","https://openalex.org/W2330064022","https://openalex.org/W4254773097","https://openalex.org/W4300477769"],"related_works":["https://openalex.org/W2394239232","https://openalex.org/W2101714536","https://openalex.org/W1965619029","https://openalex.org/W2520461891","https://openalex.org/W2339866760","https://openalex.org/W3214458670","https://openalex.org/W1983924943","https://openalex.org/W1526668334","https://openalex.org/W2055410928","https://openalex.org/W3197618938"],"abstract_inverted_index":{"The":[0,67],"canard":[1,63],"phenomenon":[2,64],"is":[3,56,65,75,171],"robust":[4],"in":[5,26,53,92,104],"singular":[6,133],"perturbation":[7,134],"problems":[8],"that":[9,79,169],"have":[10,49],"an":[11,125],"at":[12],"least":[13],"2-dimensional":[14],"folded":[15,23,30,43,68,83,86],"critical":[16],"manifold.":[17],"Canards":[18],"are":[19,112],"closely":[20],"associated":[21],"with":[22],"singularities":[24],"and,":[25],"the":[27,57,62,76,97,121,138,146,153,163,179],"case":[28],"of":[29,37,70,106,140,148,155,175],"nodes,":[31],"lead":[32],"to":[33,82],"a":[34,172],"local":[35,122],"twisting":[36],"invariant":[38],"manifolds.":[39],"Folded":[40],"node":[41],"canards,":[42,45,156,158],"saddle":[44],"and":[46,85,88,103,137,159,177],"their":[47,160],"bifurcations":[48,142],"been":[50,90],"studied":[51],"extensively":[52],"$\\mathbb{R}^3$,":[54],"which":[55,61],"minimal":[58],"dimension":[59],"for":[60],"generic.":[66],"saddle-node":[69],"type":[71],"I":[72,127],"(FSN":[73],"I)":[74],"codimension-1":[77],"bifurcation":[78],"gives":[80],"rise":[81],"nodes":[84],"saddles":[87],"has":[89],"observed":[91],"various":[93],"applications,":[94],"such":[95],"as":[96],"forced":[98],"Van":[99],"der":[100],"Pol":[101],"oscillator":[102],"models":[105],"neural":[107],"excitability.":[108],"Their":[109],"dynamics,":[110],"however,":[111],"not":[113],"completely":[114],"understood.":[115],"In":[116],"this":[117],"work,":[118],"we":[119],"analyze":[120],"dynamics":[123],"near":[124,162],"FSN":[126,164],"by":[128],"combining":[129],"methods":[130],"from":[131],"geometric":[132],"theory":[135,139],"(blow-up)":[136],"dynamic":[141],"(analytic":[143],"continuation":[144],"into":[145],"plane":[147],"complex":[149],"time).":[150],"We":[151,166],"prove":[152],"existence":[154],"faux":[157],"concatenations":[161],"I.":[165],"also":[167],"show":[168],"there":[170],"delayed":[173],"loss":[174],"stability":[176],"estimate":[178],"expected":[180],"delay.":[181]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
