{"id":"https://openalex.org/W2024858188","doi":"https://doi.org/10.1137/030601995","title":"Existence and Bifurcation of Canards in $\\mathbbR^3$ in the Case of a Folded Node","display_name":"Existence and Bifurcation of Canards in $\\mathbbR^3$ in the Case of a Folded Node","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2024858188","doi":"https://doi.org/10.1137/030601995","mag":"2024858188"},"language":"en","primary_location":{"id":"doi:10.1137/030601995","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030601995","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":["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/A5089288259","display_name":"Martin Wechselberger","orcid":"https://orcid.org/0000-0003-2681-3440"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Martin Wechselberger","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5089288259"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.9289,"has_fulltext":false,"cited_by_count":277,"citation_normalized_percentile":{"value":0.97005022,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"4","issue":"1","first_page":"101","last_page":"139"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":1.0,"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":1.0,"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":0.9995999932289124,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7515106797218323},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6447672247886658},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6247608661651611},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5902024507522583},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5573124289512634},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.5459325909614563},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.530953586101532},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5039815306663513},{"id":"https://openalex.org/keywords/singularity-theory","display_name":"Singularity theory","score":0.4877046048641205},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45877110958099365},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4568941593170166},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33236902952194214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28966712951660156},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16141921281814575},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0842430591583252}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7515106797218323},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6447672247886658},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6247608661651611},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5902024507522583},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5573124289512634},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.5459325909614563},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.530953586101532},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5039815306663513},{"id":"https://openalex.org/C207769094","wikidata":"https://www.wikidata.org/wiki/Q4245771","display_name":"Singularity theory","level":3,"score":0.4877046048641205},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45877110958099365},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4568941593170166},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33236902952194214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28966712951660156},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16141921281814575},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0842430591583252},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/030601995","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030601995","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W575067585","https://openalex.org/W1484182740","https://openalex.org/W1965778005","https://openalex.org/W1965780186","https://openalex.org/W1983924943","https://openalex.org/W1985940938","https://openalex.org/W1986739294","https://openalex.org/W2002570644","https://openalex.org/W2007339642","https://openalex.org/W2008187346","https://openalex.org/W2011459128","https://openalex.org/W2016767879","https://openalex.org/W2018250376","https://openalex.org/W2050162047","https://openalex.org/W2057545369","https://openalex.org/W2061191702","https://openalex.org/W2063827672","https://openalex.org/W2064196255","https://openalex.org/W2067063632","https://openalex.org/W2086373130","https://openalex.org/W2131038668","https://openalex.org/W2143619350","https://openalex.org/W2146926264","https://openalex.org/W2530564444"],"related_works":["https://openalex.org/W2501127101","https://openalex.org/W2135289285","https://openalex.org/W2071889957","https://openalex.org/W1988845820","https://openalex.org/W1995298252","https://openalex.org/W4245662970","https://openalex.org/W1638331504","https://openalex.org/W2380258780","https://openalex.org/W104529649","https://openalex.org/W1989798869"],"abstract_inverted_index":{"We":[0,57,68,115],"give":[1,69],"a":[2,34,70,85,100,107,133],"geometric":[3,72],"analysis":[4],"of":[5,7,27,45,48,53,64,74,80,88,99,119,135,147,151,159,161],"canards":[6,30,66,89,122,160],"folded":[8,18,51,162],"node":[9,163],"type":[10],"in":[11],"singularly":[12],"perturbed":[13],"systems":[14],"with":[15,138],"two-dimensional":[16],"(2D)":[17],"critical":[19],"manifold":[20],"using":[21,77],"the":[22,43,46,49,54,97,117,125,144,148,152,157],"blow-up":[23],"technique.":[24],"The":[25],"existence":[26,98,118,158],"two":[28],"primary":[29],"is":[31,38],"known":[32],"provided":[33],"nonresonance":[35],"condition":[36],"$\\mu\\notin\\mathbb{N}$":[37],"satisfied,":[39],"where":[40],"$\\mu=\\lambda_1/\\lambda_2$":[41],"denotes":[42],"ratio":[44],"eigenvalues":[47],"associated":[50],"singularity":[52],"reduced":[55],"flow.":[56],"show":[58,95],"that,":[59],"due":[60,155],"to":[61,83,113,132,156],"resonances,":[62],"bifurcation":[63,87,102,111],"secondary":[65,121],"occurs.":[67],"detailed":[71],"explanation":[73],"this":[75],"phenomenon":[76],"an":[78],"extension":[79],"Melnikov":[81],"theory":[82],"prove":[84],"transcritical":[86],"for":[90,103],"odd":[91],"$\\mu$.":[92],"Furthermore,":[93],"we":[94,128],"numerically":[96],"pitchfork":[101],"even":[104],"$\\mu$":[105],"and":[106,142],"novel":[108],"turning":[109],"point":[110],"close":[112],"$\\mu\\in\\mathbb{N}$.":[114],"conclude":[116],"$[(\\mu-1)/2]$":[120],"away":[123],"from":[124],"resonances.":[126],"Finally,":[127],"apply":[129],"our":[130],"results":[131],"network":[134,154],"Hodgkin--Huxley":[136],"neurons":[137],"excitatory":[139],"synaptic":[140],"coupling":[141],"explain":[143],"observed":[145],"slowing":[146],"firing":[149],"rate":[150],"synchronized":[153],"type.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":25},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":17}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}
