{"id":"https://openalex.org/W2041234363","doi":"https://doi.org/10.1137/110832392","title":"Noise-Induced Behaviors in Neural Mean Field Dynamics","display_name":"Noise-Induced Behaviors in Neural Mean Field Dynamics","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2041234363","doi":"https://doi.org/10.1137/110832392","mag":"2041234363"},"language":"en","primary_location":{"id":"doi:10.1137/110832392","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832392","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/1104.5425","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008225248","display_name":"Jonathan Touboul","orcid":"https://orcid.org/0000-0003-1366-0414"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jonathan Touboul","raw_affiliation_strings":["NEUROMATHCOMP"],"affiliations":[{"raw_affiliation_string":"NEUROMATHCOMP","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087457626","display_name":"Geoffroy Hermann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Geoffroy Hermann","raw_affiliation_strings":["NEUROMATHCOMP"],"affiliations":[{"raw_affiliation_string":"NEUROMATHCOMP","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006464572","display_name":"Olivier Faugeras","orcid":"https://orcid.org/0000-0001-8363-1550"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olivier Faugeras","raw_affiliation_strings":["NEUROMATHCOMP"],"affiliations":[{"raw_affiliation_string":"NEUROMATHCOMP","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008225248"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5892,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":{"value":0.96681104,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"11","issue":"1","first_page":"49","last_page":"81"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9998000264167786,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9994999766349792,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6327383518218994},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6156758666038513},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5859649181365967},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5773955583572388},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5417985320091248},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5406747460365295},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.5008699893951416},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.4548717737197876},{"id":"https://openalex.org/keywords/collective-behavior","display_name":"Collective behavior","score":0.442921906709671},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.42809516191482544},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.423429399728775},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.37900617718696594},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37631621956825256},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32768136262893677},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3155353367328644},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26749956607818604},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10238948464393616}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6327383518218994},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6156758666038513},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5859649181365967},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5773955583572388},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5417985320091248},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5406747460365295},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.5008699893951416},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.4548717737197876},{"id":"https://openalex.org/C100339178","wikidata":"https://www.wikidata.org/wiki/Q2548752","display_name":"Collective behavior","level":2,"score":0.442921906709671},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.42809516191482544},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.423429399728775},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.37900617718696594},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37631621956825256},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32768136262893677},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3155353367328644},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26749956607818604},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10238948464393616},{"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/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/110832392","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832392","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:arXiv.org:1104.5425","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1104.5425","pdf_url":"https://arxiv.org/pdf/1104.5425","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.767.4363","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.767.4363","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1104.5425.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00845597v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-00845597","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Dynamical Systems, 2012, 11 (1), pp.49-81. ⟨10.1137/110832392⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-00846146v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-00846146","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2011","raw_type":"Preprints, Working Papers, ..."}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1104.5425","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1104.5425","pdf_url":"https://arxiv.org/pdf/1104.5425","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W199686999","https://openalex.org/W1490778550","https://openalex.org/W1512746852","https://openalex.org/W1542782021","https://openalex.org/W1582051163","https://openalex.org/W1802196594","https://openalex.org/W1975676204","https://openalex.org/W1977297009","https://openalex.org/W1983960123","https://openalex.org/W1992476998","https://openalex.org/W1994933289","https://openalex.org/W2010228425","https://openalex.org/W2012330198","https://openalex.org/W2016354087","https://openalex.org/W2029374903","https://openalex.org/W2032123789","https://openalex.org/W2034525416","https://openalex.org/W2043361619","https://openalex.org/W2045136973","https://openalex.org/W2055649245","https://openalex.org/W2064720006","https://openalex.org/W2065172718","https://openalex.org/W2069285223","https://openalex.org/W2070765152","https://openalex.org/W2072700524","https://openalex.org/W2073937499","https://openalex.org/W2075510082","https://openalex.org/W2081696580","https://openalex.org/W2087231528","https://openalex.org/W2089876099","https://openalex.org/W2092356747","https://openalex.org/W2094930158","https://openalex.org/W2095590702","https://openalex.org/W2101465094","https://openalex.org/W2112332687","https://openalex.org/W2113345172","https://openalex.org/W2115354531","https://openalex.org/W2129207384","https://openalex.org/W2131019573","https://openalex.org/W2131215403","https://openalex.org/W2134831221","https://openalex.org/W2142981802","https://openalex.org/W2149618862","https://openalex.org/W2151740575","https://openalex.org/W2157586156","https://openalex.org/W2158374803","https://openalex.org/W2158424806","https://openalex.org/W2159128225","https://openalex.org/W2159496596","https://openalex.org/W2162515722","https://openalex.org/W2169896642","https://openalex.org/W2170482258","https://openalex.org/W2189101238","https://openalex.org/W2483090324"],"related_works":["https://openalex.org/W2371448224","https://openalex.org/W3134495997","https://openalex.org/W2363680170","https://openalex.org/W2376428685","https://openalex.org/W4320924209","https://openalex.org/W2952444919","https://openalex.org/W2036330223","https://openalex.org/W1976967990","https://openalex.org/W2498369366","https://openalex.org/W4312782710"],"abstract_inverted_index":{"The":[0],"collective":[1,158,213,247],"behavior":[2],"of":[3,12,17,29,34,49,59,85,110,131,140,154,167,181,184,205,220,225,232,243,249],"cortical":[4],"neurons":[5,36,60],"is":[6],"strongly":[7],"affected":[8],"by":[9],"the":[10,15,57,82,86,99,123,129,132,138,152,157,168,173,182,185,203,208,221,241],"presence":[11],"noise":[13,155,206,244],"at":[14],"level":[16,204],"individual":[18],"cells.":[19],"In":[20,198],"order":[21],"to":[22,45,62,120,165],"study":[23,121,151],"these":[24,141,162],"phenomena":[25,258],"in":[26,96,207,245,260],"large-scale":[27],"assemblies":[28],"neurons,":[30,250],"we":[31,147,200],"consider":[32],"networks":[33],"firing-rate":[35],"with":[37],"linear":[38],"intrinsic":[39],"dynamics":[40,248],"and":[41,52,103,128,149,160,228,251],"nonlinear":[42,111],"coupling,":[43],"belonging":[44],"a":[46,74,107,194],"few":[47,195],"types":[48],"cell":[50],"populations":[51],"receiving":[53],"noisy":[54],"currents.":[55],"As":[56],"number":[58],"tends":[61],"infinity,":[63],"asymptotic":[64,163],"equations":[65,78,114,176,187],"(mean":[66],"field":[67,175],"equations)":[68],"are":[69,79,101,117],"rigorously":[70],"derived":[71],"based":[72],"on":[73,81,144,156,240],"probabilistic":[75],"approach.":[76],"These":[77,235],"implicit":[80],"probability":[83],"distribution":[84],"solutions,":[87],"which":[88,116],"generally":[89],"makes":[90],"their":[91,104],"direct":[92],"analysis":[93],"difficult.":[94],"However,":[95],"our":[97],"case,":[98],"solutions":[100,139,183],"Gaussian,":[102],"moments":[105],"satisfy":[106],"closed":[108],"system":[109,209],"ordinary":[112],"differential":[113],"(ODEs),":[115],"much":[118],"easier":[119],"than":[122],"original":[124],"stochastic":[125],"network":[126,186,189],"equations,":[127],"statistics":[130],"empirical":[133],"process":[134],"uniformly":[135],"converge":[136],"towards":[137],"ODEs.":[142],"Based":[143],"this":[145],"description,":[146],"analytically":[148],"numerically":[150],"influence":[153],"behaviors,":[159],"compare":[161],"regimes":[164],"simulations":[166],"network.":[169],"We":[170],"observe":[171,201],"that":[172,202],"mean":[174],"provide":[177],"an":[178],"accurate":[179],"description":[180],"for":[188,216,255],"sizes":[190],"as":[191,193],"small":[192],"hundred":[196],"neurons.":[197],"particular,":[199],"qualitatively":[210],"modifies":[211],"its":[212],"behavior,":[214],"producing,":[215],"instance,":[217],"synchronized":[218],"oscillations":[219],"whole":[222],"network,":[223],"desynchronization":[224],"oscillating":[226],"regimes,":[227],"stabilization":[229],"or":[230],"destabilization":[231],"stationary":[233],"solutions.":[234],"results":[236],"shed":[237],"new":[238],"light":[239],"role":[242],"shaping":[246],"give":[252],"us":[253],"clues":[254],"understanding":[256],"similar":[257],"observed":[259],"biological":[261],"networks.":[262]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":19},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}