{"id":"https://openalex.org/W2177035502","doi":"https://doi.org/10.1137/140981770","title":"Averaging, Folded Singularities, and Torus Canards: Explaining Transitions between Bursting and Spiking in a Coupled Neuron Model","display_name":"Averaging, Folded Singularities, and Torus Canards: Explaining Transitions between Bursting and Spiking in a Coupled Neuron Model","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2177035502","doi":"https://doi.org/10.1137/140981770","mag":"2177035502"},"language":"en","primary_location":{"id":"doi:10.1137/140981770","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140981770","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/A5015063604","display_name":"Kerry-Lyn Roberts","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kerry-Lyn Roberts","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064289022","display_name":"Jonathan E. Rubin","orcid":"https://orcid.org/0000-0002-1513-1551"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jonathan E. Rubin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5089288259","display_name":"Martin Wechselberger","orcid":"https://orcid.org/0000-0003-2681-3440"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Wechselberger","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":2.5516,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.8928217,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"14","issue":"4","first_page":"1808","last_page":"1844"},"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/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"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bursting","display_name":"Bursting","score":0.8204396367073059},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.771881103515625},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.7421613931655884},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7287164330482483},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6102105379104614},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5636545419692993},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5561444163322449},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.5154884457588196},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.46587273478507996},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4267078936100006},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3762815296649933},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.37315571308135986},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3438768982887268},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2660810351371765},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22056961059570312},{"id":"https://openalex.org/keywords/neuroscience","display_name":"Neuroscience","score":0.07255959510803223}],"concepts":[{"id":"https://openalex.org/C195221683","wikidata":"https://www.wikidata.org/wiki/Q5000649","display_name":"Bursting","level":2,"score":0.8204396367073059},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.771881103515625},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7421613931655884},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7287164330482483},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6102105379104614},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5636545419692993},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5561444163322449},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.5154884457588196},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.46587273478507996},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4267078936100006},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3762815296649933},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37315571308135986},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3438768982887268},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2660810351371765},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22056961059570312},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.07255959510803223},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140981770","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140981770","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1204777979","https://openalex.org/W1484182740","https://openalex.org/W1940618937","https://openalex.org/W1967771793","https://openalex.org/W1973909460","https://openalex.org/W1987576052","https://openalex.org/W1990972851","https://openalex.org/W2000349972","https://openalex.org/W2000505932","https://openalex.org/W2009834042","https://openalex.org/W2016031811","https://openalex.org/W2024858188","https://openalex.org/W2041579436","https://openalex.org/W2057870637","https://openalex.org/W2060756826","https://openalex.org/W2063341797","https://openalex.org/W2067245612","https://openalex.org/W2069773542","https://openalex.org/W2089995439","https://openalex.org/W2093685279","https://openalex.org/W2093823001","https://openalex.org/W2099533877","https://openalex.org/W2103078370","https://openalex.org/W2109607999","https://openalex.org/W2119407299","https://openalex.org/W2120574708","https://openalex.org/W2152707060","https://openalex.org/W2220903811"],"related_works":["https://openalex.org/W2080788537","https://openalex.org/W3181055709","https://openalex.org/W2002830460","https://openalex.org/W2064213689","https://openalex.org/W2036451364","https://openalex.org/W3195397619","https://openalex.org/W4243975172","https://openalex.org/W2165689100","https://openalex.org/W1976788707","https://openalex.org/W2020121147"],"abstract_inverted_index":{"In":[0],"this":[1,98],"work,":[2],"we":[3,28],"identify":[4],"generic":[5],"bifurcation":[6],"scenarios":[7],"corresponding":[8],"to":[9,100],"transitions":[10,116],"between":[11],"bursting":[12],"and":[13,27,52,106,108],"tonic":[14],"spiking":[15],"solutions":[16,72],"in":[17,36,42,46,79,93],"a":[18,21,63],"model":[19],"for":[20],"coupled":[22],"pair":[23],"of":[24,33,49,60,67,114],"burst-capable":[25],"neurons,":[26],"elucidate":[29],"the":[30,47,58,112],"central":[31],"role":[32],"folded":[34,40],"singularities":[35,41],"these":[37],"scenarios.":[38],"The":[39],"our":[43,54,95],"work":[44,96],"arise":[45],"context":[48],"fast-slow":[50],"averaging,":[51],"hence":[53],"results":[55],"link":[56],"with":[57],"study":[59,99],"torus":[61],"canards,":[62],"recently":[64],"identified":[65],"class":[66],"ordinary":[68],"differential":[69],"equation":[70],"(ODE)":[71],"featuring":[73,102],"oscillatory":[74],"excursions":[75],"along":[76],"repelling":[77],"structures":[78],"phase":[80],"space":[81],"[J.":[82],"Burke":[83],"et":[84,120],"al.,":[85],"J.":[86,123],"Math.":[87],"Neurosci.,":[88],"2":[89],"(2012),":[90],"pp.":[91,129],"1--30];":[92],"particular,":[94],"extends":[97],"systems":[101],"two":[103],"slow":[104],"variables":[105],"symmetry":[107],"goes":[109],"significantly":[110],"beyond":[111],"analysis":[113],"activity":[115],"presented":[117],"by":[118],"Best":[119],"al.":[121],"[SIAM":[122],"Appl.":[124],"Dyn.":[125],"Syst.,":[126],"4":[127],"(2005),":[128],"1107--1139].":[130]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}