{"id":"https://openalex.org/W2034307400","doi":"https://doi.org/10.1137/100809866","title":"Canard-Like Explosion of Limit Cycles in Two-Dimensional Piecewise-Linear Models of FitzHugh\u2013Nagumo Type","display_name":"Canard-Like Explosion of Limit Cycles in Two-Dimensional Piecewise-Linear Models of FitzHugh\u2013Nagumo Type","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2034307400","doi":"https://doi.org/10.1137/100809866","mag":"2034307400"},"language":"en","primary_location":{"id":"doi:10.1137/100809866","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100809866","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/A5046627918","display_name":"Horacio G. Rotstein","orcid":"https://orcid.org/0000-0002-4387-5160"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Horacio G. Rotstein","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015605154","display_name":"Stephen Coombes","orcid":"https://orcid.org/0000-0003-1610-7665"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stephen Coombes","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5010155132","display_name":"Ana Maria Gheorghe","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ana Maria Gheorghe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.625,"has_fulltext":false,"cited_by_count":73,"citation_normalized_percentile":{"value":0.93512046,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"1","first_page":"135","last_page":"180"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9986000061035156,"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":0.9975000023841858,"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":0.6144852638244629},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5932671427726746},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5778650641441345},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.576634407043457},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5637466907501221},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.5545687079429626},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5322067141532898},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.4948236346244812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4836176931858063},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.43114209175109863},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3948037326335907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3858579397201538},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3471081852912903}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6144852638244629},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5932671427726746},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5778650641441345},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.576634407043457},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5637466907501221},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.5545687079429626},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5322067141532898},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4948236346244812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4836176931858063},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.43114209175109863},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3948037326335907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3858579397201538},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3471081852912903},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"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},{"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:10.1137/100809866","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100809866","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":45,"referenced_works":["https://openalex.org/W58398526","https://openalex.org/W106033737","https://openalex.org/W207692870","https://openalex.org/W653690259","https://openalex.org/W1494104450","https://openalex.org/W1551791849","https://openalex.org/W1552277675","https://openalex.org/W1588906117","https://openalex.org/W1592648094","https://openalex.org/W1876456565","https://openalex.org/W1888008771","https://openalex.org/W1967848725","https://openalex.org/W1981990904","https://openalex.org/W1982713952","https://openalex.org/W1983920324","https://openalex.org/W1986739294","https://openalex.org/W1988934258","https://openalex.org/W1990076160","https://openalex.org/W1993068124","https://openalex.org/W2002282594","https://openalex.org/W2004312437","https://openalex.org/W2009375605","https://openalex.org/W2028118090","https://openalex.org/W2031356502","https://openalex.org/W2032728482","https://openalex.org/W2054505297","https://openalex.org/W2055091670","https://openalex.org/W2064196255","https://openalex.org/W2065441439","https://openalex.org/W2068736542","https://openalex.org/W2084730754","https://openalex.org/W2089995439","https://openalex.org/W2090896255","https://openalex.org/W2092566320","https://openalex.org/W2104426272","https://openalex.org/W2108331166","https://openalex.org/W2122576752","https://openalex.org/W2134072465","https://openalex.org/W2134504489","https://openalex.org/W2143557716","https://openalex.org/W2143976842","https://openalex.org/W2145281112","https://openalex.org/W2153904027","https://openalex.org/W2599590817","https://openalex.org/W4254773097"],"related_works":["https://openalex.org/W4388297534","https://openalex.org/W2051439117","https://openalex.org/W1673883441","https://openalex.org/W4298109871","https://openalex.org/W2313188567","https://openalex.org/W4248124207","https://openalex.org/W2083477739","https://openalex.org/W2087320822","https://openalex.org/W2089966216","https://openalex.org/W2017930464"],"abstract_inverted_index":{"We":[0,168],"investigate":[1,121],"the":[2,23,51,61,68,81,88,101,117,122,127,132,149,160,163,204],"mechanism":[3,128],"of":[4,18,25,103,109,147,152,162,178,206,209],"abrupt":[5],"transition":[6,135],"between":[7,87,136],"small-":[8],"and":[9,34,64,70,90,139,141,211,218],"large":[10],"amplitude":[11,150],"oscillations":[12,33,138],"in":[13,60,67,80],"fast-slow":[14],"piecewise-linear":[15],"(PWL)":[16],"models":[17,74,108,173,185],"FitzHugh\u2013Nagumo":[19],"(FHN)":[20],"type.":[21],"In":[22,195],"context":[24],"neuroscience,":[26],"these":[27],"oscillatory":[28,98],"regimes":[29],"correspond":[30],"to":[31,131,172],"subthreshold":[32,137],"action":[35],"potentials":[36],"(spikes),":[37],"respectively.":[38],"The":[39],"minimal":[40,118],"model":[41,119],"that":[42,129,200],"shows":[43],"such":[44],"phenomena":[45],"has":[46],"a":[47,85,96,153,175,207],"cubic-like":[48],"nullcline":[49],"(for":[50],"fast":[52],"equation)":[53],"with":[54,75,174,188],"two":[55],"or":[56,84],"more":[57,212],"linear":[58,78,104,179],"pieces":[59,105],"middle":[62,82],"branch":[63,83],"one":[65,77],"piece":[66,79],"left":[69,89],"right":[71,91],"branches.":[72],"Simpler":[73],"only":[76],"discontinuity":[86],"branches":[92],"(McKean":[93],"model)":[94],"show":[95],"single":[97],"mode.":[99],"As":[100],"number":[102,177],"increases,":[106],"PWL":[107],"FHN":[110],"type":[111],"approach":[112],"smooth":[113,192],"FHN-type":[114,193],"models.":[115,194],"For":[116],"we":[120,125,142,197],"bifurcation":[123],"structure;":[124],"describe":[126],"leads":[130],"abrupt,":[133],"canard-like":[134],"spikes;":[140],"provide":[143],"an":[144],"analytical":[145],"way":[146],"predicting":[148],"regime":[151],"given":[154],"limit":[155],"cycle":[156],"trajectory":[157],"which":[158],"includes":[159],"approximation":[161],"canard":[164],"critical":[165],"control":[166],"parameter.":[167],"extend":[169],"our":[170],"results":[171,182,190],"larger":[176],"pieces.":[180],"Our":[181],"for":[183,191,203],"PWL-FHN-type":[184],"are":[186,201],"consistent":[187],"similar":[189],"addition,":[196],"develop":[198],"tools":[199],"amenable":[202],"investigation":[205],"variety":[208],"related,":[210],"complex,":[213],"problems":[214],"including":[215],"forced,":[216],"stochastic,":[217],"coupled":[219],"oscillators.":[220]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-08-19T15:00:24.278416","created_date":"2025-10-10T00:00:00"}