{"id":"https://openalex.org/W2274532073","doi":"https://doi.org/10.1137/16m1061813","title":"Quantifying Noisy Attractors: From Heteroclinic to Excitable Networks","display_name":"Quantifying Noisy Attractors: From Heteroclinic to Excitable Networks","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2274532073","doi":"https://doi.org/10.1137/16m1061813","mag":"2274532073"},"language":"en","primary_location":{"id":"doi:10.1137/16m1061813","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1061813","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/1602.06135","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Peter Ashwin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter Ashwin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Claire Postlethwaite","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Claire Postlethwaite","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":1.7366,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.88516563,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"4","first_page":"1989","last_page":"2016"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.12269999831914902,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.12269999831914902,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.11309999972581863,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.07580000162124634,"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/attractor","display_name":"Attractor","score":0.6610999703407288},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5249000191688538},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5008999705314636},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4887000024318695},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.4767000079154968},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.45660001039505005},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.453900009393692},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.39910000562667847},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.39250001311302185}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6610999703407288},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5670999884605408},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5249000191688538},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5008999705314636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49140000343322754},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4887000024318695},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4767000079154968},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.45660001039505005},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.453900009393692},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.39910000562667847},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.39250001311302185},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.38040000200271606},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3635999858379364},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.357699990272522},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.34630000591278076},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C2780042749","wikidata":"https://www.wikidata.org/wiki/Q604374","display_name":"Kuramoto model","level":4,"score":0.31049999594688416},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30390000343322754},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C2780186347","wikidata":"https://www.wikidata.org/wiki/Q11414","display_name":"Subnetwork","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C2775913793","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Residence time (fluid dynamics)","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.27399998903274536},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.2669999897480011},{"id":"https://openalex.org/C104122410","wikidata":"https://www.wikidata.org/wiki/Q1416406","display_name":"Network model","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/16m1061813","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1061813","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:ore.exeter.ac.uk:10871/23186","is_oa":false,"landing_page_url":"http://hdl.handle.net/10871/23186","pdf_url":null,"source":{"id":"https://openalex.org/S4306401998","display_name":"Open Research Exeter (University of Exeter)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I23923803","host_organization_name":"University of Exeter","host_organization_lineage":["https://openalex.org/I23923803"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:ore.exeter.ac.uk:10871/26670","is_oa":false,"landing_page_url":"http://hdl.handle.net/10871/26670","pdf_url":null,"source":{"id":"https://openalex.org/S4306401998","display_name":"Open Research Exeter (University of Exeter)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I23923803","host_organization_name":"University of Exeter","host_organization_lineage":["https://openalex.org/I23923803"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1602.06135","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.06135","pdf_url":"https://arxiv.org/pdf/1602.06135","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:1602.06135","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.06135","pdf_url":"https://arxiv.org/pdf/1602.06135","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/G1436783943","display_name":null,"funder_award_id":"EP/N014391/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G688401098","display_name":"EPSRC Centre for Predictive Modelling in Healthcare","funder_award_id":"EP/N014391/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1972211900","https://openalex.org/W1995553186","https://openalex.org/W1999637900","https://openalex.org/W2004550467","https://openalex.org/W2006672103","https://openalex.org/W2007771207","https://openalex.org/W2010242617","https://openalex.org/W2012102499","https://openalex.org/W2017231791","https://openalex.org/W2018394408","https://openalex.org/W2056199650","https://openalex.org/W2064645897","https://openalex.org/W2070218723","https://openalex.org/W2072319634","https://openalex.org/W2072700524","https://openalex.org/W2116967254","https://openalex.org/W2153170491","https://openalex.org/W2161853585","https://openalex.org/W2282093328"],"related_works":[],"abstract_inverted_index":{"Attractors":[0],"of":[1,47,54,57,64,67,75,95,128,131,141,198,207,213,219,235,269],"dynamical":[2,17,35],"systems":[3],"may":[4],"be":[5,12,31,254],"networks":[6,110],"in":[7,52,62,116,138,210,257],"phase":[8,58],"space":[9,59],"that":[10,224,251,277],"can":[11,42,80,114,230,253],"heteroclinic":[13,157],"(where":[14,25,185],"there":[15],"are":[16,77,111],"connections":[18],"between":[19,37,194,205],"simple":[20],"invariant":[21],"sets)":[22],"or":[23,227],"excitable":[24,167],"a":[26,34,44,146,173,225],"perturbation":[27],"threshold":[28],"needs":[29],"to":[30,33,49,83,91,163,177,189,281],"crossed":[32],"connection":[36],"\u201cnodes'').":[38],"Such":[39],"network":[40,76,100,158,168,209,229,260,284],"attractors":[41,285],"display":[43],"high":[45],"degree":[46],"sensitivity":[48],"noise":[50,97,142],"both":[51],"terms":[53,63],"the":[55,65,70,84,93,104,109,121,139,149,166,192,195,208,211,246,267,273],"regions":[56],"visited":[60],"and":[61,113,238,291],"sequence":[66],"transitions":[68],"around":[69,120],"network.":[71,122,199],"The":[72,156],"two":[73,196],"types":[74,197],"intimately":[78],"related---one":[79],"directly":[81],"bifurcate":[82],"other.":[85],"In":[86],"this":[87,252],"paper":[88],"we":[89],"attempt":[90],"quantify":[92],"effect":[94],"additive":[96],"on":[98],"such":[99],"attractors.":[101],"Noise":[102],"increases":[103],"average":[105],"rate":[106],"at":[107,191,245],"which":[108],"explored":[112],"result":[115],"\u201cmacroscopic\u201d":[117],"random":[118],"motion":[119],"We":[123,200,249],"perform":[124],"an":[125,132],"asymptotic":[126],"analysis":[127],"local":[129],"behavior":[130,184],"escape":[133,264,271],"model":[134,147],"near":[135,154],"heteroclinic/excitable":[136],"nodes":[137,206],"limit":[140],"$\\eta\\rightarrow":[143],"0^+$":[144],"as":[145],"for":[148],"mean":[150,242],"residence":[151,243,292],"time":[152],"$T$":[153,161,170,186],"equilibria.":[155],"case":[159],"has":[160,169],"proportional":[162,176,188],"$-\\ln\\eta$":[164],"while":[165],"given":[171,247],"by":[172,261],"Kramers'":[174],"law,":[175],"$\\exp":[178],"(B/\\eta^2)$.":[179],"There":[180],"is":[181,187,279],"singular":[182],"scaling":[183],"$1/\\eta$)":[190],"bifurcation":[193],"also":[201],"explore":[202],"transition":[203,236,289],"probabilities":[204,237,290],"presence":[212],"anisotropic":[214],"noise.":[215],"For":[216],"low":[217],"levels":[218],"noise,":[220],"numerical":[221],"results":[222],"suggest":[223],"(heteroclinic":[226],"excitable)":[228],"approximately":[231],"realize":[232],"any":[233,239],"set":[234],"sufficiently":[240],"large":[241],"times":[244],"nodes.":[248],"show":[250],"well":[255],"modeled":[256],"our":[258],"example":[259],"multiple":[262],"independent":[263],"processes,":[265],"where":[266],"direction":[268],"first":[270],"determines":[272],"transition.":[274],"This":[275],"suggests":[276],"it":[278],"feasible":[280],"design":[282],"noisy":[283],"with":[286],"arbitrary":[287],"Markov":[288],"times.":[293]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2016-06-24T00:00:00"}