{"id":"https://openalex.org/W7154973115","doi":"https://doi.org/10.3389/fncom.2026.1762692","title":"Deterministic, stochastic, and mean-field PDE models in neuroscience","display_name":"Deterministic, stochastic, and mean-field PDE models in neuroscience","publication_year":2026,"publication_date":"2026-04-20","ids":{"openalex":"https://openalex.org/W7154973115","doi":"https://doi.org/10.3389/fncom.2026.1762692","pmid":"https://pubmed.ncbi.nlm.nih.gov/42088462"},"language":"en","primary_location":{"id":"doi:10.3389/fncom.2026.1762692","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fncom.2026.1762692","pdf_url":"https://public-pages-files-2025.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2026.1762692/pdf","source":{"id":"https://openalex.org/S19778766","display_name":"Frontiers in Computational Neuroscience","issn_l":"1662-5188","issn":["1662-5188"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computational Neuroscience","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://public-pages-files-2025.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2026.1762692/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043365454","display_name":"Co\u015fkun \u00c7etin","orcid":"https://orcid.org/0000-0001-8457-8675"},"institutions":[{"id":"https://openalex.org/I127339247","display_name":"California State University System","ror":"https://ror.org/020qm1538","country_code":"US","type":"education","lineage":["https://openalex.org/I127339247"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Co\u015fkun \u00c7etin","raw_affiliation_strings":["Department of Mathematics and Statistics, California State University, CSU"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, California State University, CSU","institution_ids":["https://openalex.org/I127339247"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134057379","display_name":"Jose Roberto Castilho Piqueira","orcid":null},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jose Roberto Castilho Piqueira","raw_affiliation_strings":["Escola Polit\u00e9cnica, Universidade de S\u00e3o Paulo"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Escola Polit\u00e9cnica, Universidade de S\u00e3o Paulo","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036590471","display_name":"Burhaneddin \u0130zgi\u0307","orcid":"https://orcid.org/0000-0002-8441-9137"},"institutions":[{"id":"https://openalex.org/I48912391","display_name":"Istanbul Technical University","ror":"https://ror.org/059636586","country_code":"TR","type":"education","lineage":["https://openalex.org/I48912391"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Burhaneddin \u0130zgi","raw_affiliation_strings":["Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University","institution_ids":["https://openalex.org/I48912391"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051155059","display_name":"Ay\u015fe Peker-Dobie","orcid":null},"institutions":[{"id":"https://openalex.org/I48912391","display_name":"Istanbul Technical University","ror":"https://ror.org/059636586","country_code":"TR","type":"education","lineage":["https://openalex.org/I48912391"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Ayse Peker-Dobie","raw_affiliation_strings":["Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University","institution_ids":["https://openalex.org/I48912391"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051459984","display_name":"Semra Ahmetolan","orcid":"https://orcid.org/0000-0003-1003-7918"},"institutions":[{"id":"https://openalex.org/I48912391","display_name":"Istanbul Technical University","ror":"https://ror.org/059636586","country_code":"TR","type":"education","lineage":["https://openalex.org/I48912391"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Semra Ahmetolan","raw_affiliation_strings":["Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University","institution_ids":["https://openalex.org/I48912391"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012125620","display_name":"Murat \u00d6zkaya","orcid":"https://orcid.org/0000-0001-7241-4710"},"institutions":[{"id":"https://openalex.org/I115953327","display_name":"\u00c7anakkale Onsekiz Mart \u00dcniversitesi","ror":"https://ror.org/05rsv8p09","country_code":"TR","type":"education","lineage":["https://openalex.org/I115953327"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Murat \u00d6zkaya","raw_affiliation_strings":["Department of Business, Faculty of Political Sciences, \u00c7anakkale Onsekiz Mart University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Business, Faculty of Political Sciences, \u00c7anakkale Onsekiz Mart University","institution_ids":["https://openalex.org/I115953327"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2950,"currency":"USD","value_usd":2950},"apc_paid":{"value":2950,"currency":"USD","value_usd":2950},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.6141472,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":null,"first_page":"1762692","last_page":"1762692"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9168000221252441,"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":0.9168000221252441,"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":0.0210999995470047,"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/T10077","display_name":"Neuroscience and Neuropharmacology Research","score":0.009700000286102295,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular 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/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5303999781608582},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5033000111579895},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5013999938964844},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.48420000076293945},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4499000012874603},{"id":"https://openalex.org/keywords/computational-neuroscience","display_name":"Computational neuroscience","score":0.4375999867916107},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4002000093460083},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3905999958515167},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.37470000982284546}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5468000173568726},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5303999781608582},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5033000111579895},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5013999938964844},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.48420000076293945},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4499000012874603},{"id":"https://openalex.org/C15286952","wikidata":"https://www.wikidata.org/wiki/Q8037925","display_name":"Computational neuroscience","level":2,"score":0.4375999867916107},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4002000093460083},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.37470000982284546},{"id":"https://openalex.org/C2909946758","wikidata":"https://www.wikidata.org/wiki/Q194277","display_name":"Spike train","level":3,"score":0.367000013589859},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.36419999599456787},{"id":"https://openalex.org/C3832189","wikidata":"https://www.wikidata.org/wiki/Q8588916","display_name":"Models of neural computation","level":3,"score":0.3549000024795532},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3398999869823456},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3375000059604645},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C66024118","wikidata":"https://www.wikidata.org/wiki/Q1122506","display_name":"Computational model","level":2,"score":0.3075000047683716},{"id":"https://openalex.org/C177731217","wikidata":"https://www.wikidata.org/wiki/Q2622244","display_name":"Mesoscopic physics","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.2976999878883362},{"id":"https://openalex.org/C118403218","wikidata":"https://www.wikidata.org/wiki/Q43283","display_name":"Biological neural network","level":2,"score":0.29490000009536743},{"id":"https://openalex.org/C86582703","wikidata":"https://www.wikidata.org/wiki/Q7617824","display_name":"Stochastic neural network","level":4,"score":0.2930999994277954},{"id":"https://openalex.org/C117838684","wikidata":"https://www.wikidata.org/wiki/Q533483","display_name":"Local field potential","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C2781390188","wikidata":"https://www.wikidata.org/wiki/Q25203449","display_name":"Spike (software development)","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C168451700","wikidata":"https://www.wikidata.org/wiki/Q1306528","display_name":"Neural engineering","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.26269999146461487},{"id":"https://openalex.org/C2984127161","wikidata":"https://www.wikidata.org/wiki/Q969316","display_name":"Neural activity","level":2,"score":0.2619999945163727},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.25929999351501465},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2587999999523163},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.25380000472068787},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3389/fncom.2026.1762692","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fncom.2026.1762692","pdf_url":"https://public-pages-files-2025.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2026.1762692/pdf","source":{"id":"https://openalex.org/S19778766","display_name":"Frontiers in Computational Neuroscience","issn_l":"1662-5188","issn":["1662-5188"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computational Neuroscience","raw_type":"journal-article"},{"id":"pmid:42088462","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42088462","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in computational neuroscience","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:13136274","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13136274/","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13136274/pdf/fncom-20-1762692.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Front Comput Neurosci","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:e4347943723344c0891c1b83efba32e8","is_oa":true,"landing_page_url":"https://doaj.org/article/e4347943723344c0891c1b83efba32e8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Computational Neuroscience, Vol 20 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3389/fncom.2026.1762692","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fncom.2026.1762692","pdf_url":"https://public-pages-files-2025.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2026.1762692/pdf","source":{"id":"https://openalex.org/S19778766","display_name":"Frontiers in Computational Neuroscience","issn_l":"1662-5188","issn":["1662-5188"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computational Neuroscience","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7154973115.pdf","grobid_xml":"https://content.openalex.org/works/W7154973115.grobid-xml"},"referenced_works_count":113,"referenced_works":["https://openalex.org/W316919195","https://openalex.org/W416630258","https://openalex.org/W1184115476","https://openalex.org/W1503185336","https://openalex.org/W1582051163","https://openalex.org/W1621950790","https://openalex.org/W1893670732","https://openalex.org/W1940853939","https://openalex.org/W1968187292","https://openalex.org/W1968796590","https://openalex.org/W1968900640","https://openalex.org/W1969625582","https://openalex.org/W1971657654","https://openalex.org/W1973679426","https://openalex.org/W1976284739","https://openalex.org/W1985220467","https://openalex.org/W1985983039","https://openalex.org/W1989512479","https://openalex.org/W1996637707","https://openalex.org/W1998504251","https://openalex.org/W1999483147","https://openalex.org/W2002465097","https://openalex.org/W2004044411","https://openalex.org/W2006545642","https://openalex.org/W2009375605","https://openalex.org/W2016354087","https://openalex.org/W2022646653","https://openalex.org/W2022904439","https://openalex.org/W2035645686","https://openalex.org/W2046424015","https://openalex.org/W2050116116","https://openalex.org/W2050840442","https://openalex.org/W2053381107","https://openalex.org/W2054219055","https://openalex.org/W2056550744","https://openalex.org/W2061191702","https://openalex.org/W2065003781","https://openalex.org/W2068765647","https://openalex.org/W2069024199","https://openalex.org/W2069849731","https://openalex.org/W2070765152","https://openalex.org/W2076618566","https://openalex.org/W2083613130","https://openalex.org/W2092773397","https://openalex.org/W2095768716","https://openalex.org/W2098888923","https://openalex.org/W2102952547","https://openalex.org/W2112445099","https://openalex.org/W2114867602","https://openalex.org/W2117469172","https://openalex.org/W2118534045","https://openalex.org/W2120719475","https://openalex.org/W2139413555","https://openalex.org/W2146052710","https://openalex.org/W2151073193","https://openalex.org/W2154863095","https://openalex.org/W2157979498","https://openalex.org/W2158424806","https://openalex.org/W2165577901","https://openalex.org/W2168809073","https://openalex.org/W2236752435","https://openalex.org/W2417122616","https://openalex.org/W2483809583","https://openalex.org/W2547783202","https://openalex.org/W2557964287","https://openalex.org/W2590144118","https://openalex.org/W2609004733","https://openalex.org/W2616911527","https://openalex.org/W2775163164","https://openalex.org/W2805663336","https://openalex.org/W2851906854","https://openalex.org/W2886172288","https://openalex.org/W2891517012","https://openalex.org/W2904639936","https://openalex.org/W2962765420","https://openalex.org/W2979026150","https://openalex.org/W3011049743","https://openalex.org/W3033264213","https://openalex.org/W3094914387","https://openalex.org/W3125250978","https://openalex.org/W3133413237","https://openalex.org/W3176393779","https://openalex.org/W3177139890","https://openalex.org/W3194374736","https://openalex.org/W4231021340","https://openalex.org/W4231081240","https://openalex.org/W4238614602","https://openalex.org/W4247720484","https://openalex.org/W4247820434","https://openalex.org/W4253613142","https://openalex.org/W4307888737","https://openalex.org/W4311093209","https://openalex.org/W4313328893","https://openalex.org/W4323310088","https://openalex.org/W4362634436","https://openalex.org/W4376454194","https://openalex.org/W4388687715","https://openalex.org/W4388757282","https://openalex.org/W4402574424","https://openalex.org/W4403987574","https://openalex.org/W4404356183","https://openalex.org/W4404465385","https://openalex.org/W4405108788","https://openalex.org/W4405561658","https://openalex.org/W4406547668","https://openalex.org/W4411854408","https://openalex.org/W4411857322","https://openalex.org/W4413415351","https://openalex.org/W4413945779","https://openalex.org/W4414230137","https://openalex.org/W4415432676","https://openalex.org/W4416994658","https://openalex.org/W4417210115"],"related_works":[],"abstract_inverted_index":{"Large":[0],"neuronal":[1],"networks":[2],"demonstrate":[3],"complex":[4],"dynamics":[5],"across":[6],"multiple":[7],"scales,":[8],"ranging":[9],"from":[10],"single-neuron":[11,107],"excitability":[12],"and":[13,19,38,56,84,100,112,119,128,135,152,176,184,207,215,238,251,258,270],"spike-train":[14],"variability":[15,154,183],"to":[16,31,109,115,142,164,170,177,195,203],"mesoscopic":[17],"rhythms":[18],"whole-brain":[20,57],"activity.":[21,157],"Different":[22],"types":[23],"of":[24,66,91,212,222,241,273],"differential":[25,46,75,124],"equation":[26,47,76,125],"models":[27,78,127,160,197,217,257,275],"have":[28],"been":[29],"developed":[30],"comprehend":[32],"these":[33],"phenomena,":[34],"connecting":[35],"deterministic,":[36],"stochastic,":[37],"mean-field":[39,73],"descriptions.":[40],"At":[41,69],"the":[42,70,89,204,220,239,271],"deterministic":[43],"level,":[44,72],"ordinary":[45],"(ODE)":[48],"models,":[49,53],"including":[50],"conductance-based":[51],"neuron":[52],"neural-mass":[54],"systems,":[55,190],"networks,":[58],"summarize":[59],"neural":[60,85,156,165,180,189,233,243],"behavior":[61],"through":[62],"a":[63],"reduced":[64],"set":[65],"macroscopic":[67],"variables.":[68,103],"population":[71,94],"partial":[74],"(PDE)":[77],"such":[79,264],"as":[80,265],"Fokker-Planck,":[81],"age-structured,":[82],"kinetic,":[83],"field":[86],"equations":[87],"describe":[88,143],"evolution":[90],"probability":[92],"or":[93],"densities":[95],"over":[96],"membrane-potentials,":[97],"synaptic":[98,150],"states,":[99],"other":[101,120],"kinetic":[102],"These":[104,158],"PDEs":[105,137],"link":[106],"mechanisms":[108],"population-level":[110],"activity":[111],"allow":[113],"one":[114],"analyze":[116],"bifurcations,":[117],"oscillations":[118],"collective":[121],"patterns.":[122],"Stochastic":[123],"(SDE)":[126],"their":[129],"extensions":[130],"that":[131,219],"include":[132],"jump-diffusion":[133],"processes":[134],"stochastic":[136,159,196,256],"(SPDEs)":[138],"are":[139,161,186],"widely":[140],"used":[141],"random":[144],"membrane":[145],"fluctuations,":[146],"irregular":[147],"spike":[148],"trains,":[149],"plasticity":[151],"large-scale":[153],"in":[155,173,188,225],"also":[162,246],"applied":[163],"data":[166],"analysis,":[167],"for":[168,230,255],"example":[169],"quantify":[171],"noise":[172,185],"electro-physiological":[174],"recordings":[175],"infer":[178],"latent":[179],"dynamics.":[181],"Because":[182],"central":[187],"we":[191],"devote":[192],"more":[193],"space":[194],"but":[198],"always":[199],"relate":[200],"them":[201],"back":[202],"surrounding":[205],"ODE":[206],"PDE":[208],"frameworks.":[209],"This":[210],"hierarchy":[211],"ODE,":[213],"PDE,":[214],"SDE-SPDE":[216],"shows":[218],"versatility":[221],"differential-equation-based":[223],"approaches":[224],"neuroscience":[226],"offers":[227],"unified":[228],"tools":[229],"multiscale":[231,266],"modeling,":[232,237],"signal":[234],"processing,":[235],"cognitive":[236],"analysis":[240],"noisy":[242],"systems.":[244],"We":[245],"discuss":[247],"some":[248],"known":[249],"numerical":[250],"computational":[252],"approaches,":[253],"especially":[254],"conclude":[259],"by":[260],"outlining":[261],"open":[262],"challenges,":[263],"inference,":[267],"control-oriented":[268],"formulations":[269],"integration":[272],"differential-equation":[274],"with":[276],"modern":[277],"machine-learning":[278],"methods.":[279]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-21T00:00:00"}