{"id":"https://openalex.org/W2124372375","doi":"https://doi.org/10.1162/neco_a_00308","title":"Neural Dynamics, Bifurcations, and Firing Rates in a Quadratic Integrate-and-Fire Model with a Recovery Variable. I: Deterministic Behavior","display_name":"Neural Dynamics, Bifurcations, and Firing Rates in a Quadratic Integrate-and-Fire Model with a Recovery Variable. I: Deterministic Behavior","publication_year":2012,"publication_date":"2012-04-17","ids":{"openalex":"https://openalex.org/W2124372375","doi":"https://doi.org/10.1162/neco_a_00308","mag":"2124372375","pmid":"https://pubmed.ncbi.nlm.nih.gov/22509966"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_00308","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00308","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5051370791","display_name":"Eli Shlizerman","orcid":"https://orcid.org/0000-0002-3136-4531"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Eli Shlizerman","raw_affiliation_strings":["Department of Applied Mathematics, University of Washington, Seattle, WA 98195-2420, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Washington, Seattle, WA 98195-2420, U.S.A","institution_ids":["https://openalex.org/I4210138199","https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053868357","display_name":"Philip Holmes","orcid":"https://orcid.org/0000-0002-1459-7157"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Philip Holmes","raw_affiliation_strings":["Program in Applied and Computational Mathematics, Department of Mechanical and Aerospace Engineering and Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544-1000, U.S.A"],"affiliations":[{"raw_affiliation_string":"Program in Applied and Computational Mathematics, Department of Mechanical and Aerospace Engineering and Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544-1000, U.S.A","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051370791"],"corresponding_institution_ids":["https://openalex.org/I201448701","https://openalex.org/I4210138199"],"apc_list":null,"apc_paid":null,"fwci":1.2567,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.78269654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"24","issue":"8","first_page":"2078","last_page":"2118"},"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":0.9997000098228455,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9983000159263611,"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/quadratic-equation","display_name":"Quadratic equation","score":0.6428483724594116},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.593734860420227},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5855126976966858},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.5709619522094727},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4804070293903351},{"id":"https://openalex.org/keywords/reset","display_name":"Reset (finance)","score":0.4738726317882538},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.43170166015625},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.41492825746536255},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.41033995151519775},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.40454283356666565},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39961257576942444},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2686602771282196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2625202536582947},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21826264262199402},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17555314302444458},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11489173769950867},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10133463144302368},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07552754878997803}],"concepts":[{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6428483724594116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.593734860420227},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5855126976966858},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.5709619522094727},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4804070293903351},{"id":"https://openalex.org/C2779795794","wikidata":"https://www.wikidata.org/wiki/Q7315343","display_name":"Reset (finance)","level":2,"score":0.4738726317882538},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.43170166015625},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.41492825746536255},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.41033995151519775},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.40454283356666565},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39961257576942444},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2686602771282196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2625202536582947},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21826264262199402},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17555314302444458},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11489173769950867},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10133463144302368},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07552754878997803},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1162/neco_a_00308","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00308","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:22509966","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/22509966","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":"Neural computation","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W19317540","https://openalex.org/W316919195","https://openalex.org/W611428499","https://openalex.org/W1481616730","https://openalex.org/W1487210357","https://openalex.org/W1542177822","https://openalex.org/W1567812234","https://openalex.org/W1576838367","https://openalex.org/W1596321532","https://openalex.org/W1983069678","https://openalex.org/W1983694290","https://openalex.org/W1985940938","https://openalex.org/W1997576506","https://openalex.org/W2009375605","https://openalex.org/W2029342452","https://openalex.org/W2029924743","https://openalex.org/W2033365967","https://openalex.org/W2038879792","https://openalex.org/W2056661320","https://openalex.org/W2061191702","https://openalex.org/W2072413244","https://openalex.org/W2082380332","https://openalex.org/W2086633615","https://openalex.org/W2089876099","https://openalex.org/W2096519870","https://openalex.org/W2114863659","https://openalex.org/W2152502378","https://openalex.org/W2154914851","https://openalex.org/W2164653071","https://openalex.org/W2171849804","https://openalex.org/W2480701976","https://openalex.org/W2612743911","https://openalex.org/W3041070869","https://openalex.org/W3123094903","https://openalex.org/W4213388037","https://openalex.org/W4248370132"],"related_works":["https://openalex.org/W269925151","https://openalex.org/W3096788047","https://openalex.org/W2101513891","https://openalex.org/W4386731488","https://openalex.org/W2024156986","https://openalex.org/W2995216836","https://openalex.org/W2027798872","https://openalex.org/W4385817362","https://openalex.org/W2765709060","https://openalex.org/W4320232412"],"abstract_inverted_index":{"We":[0,61],"study":[1],"the":[2,39,56,73,78,96,106],"dynamics":[3],"of":[4,9,32,41,43,65,72,89,108],"a":[5,10,14,33,44,87],"quadratic":[6],"integrate-and-fire":[7],"model":[8],"single-compartment":[11],"neuron":[12],"with":[13,51,95],"slow":[15],"recovery":[16,25,74],"variable,":[17,26,75],"as":[18,86],"input":[19],"current":[20,90],"and":[21,27,76,91,112],"parameters":[22],"describing":[23],"timescales,":[24],"postspike":[28],"reset":[29,52,92],"change.":[30],"Analysis":[31],"codimension":[34],"2":[35],"bifurcation":[36],"reveals":[37],"that":[38],"domain":[40],"attraction":[42],"stable":[45],"hyperpolarized":[46],"rest":[47],"state":[48,58],"interacts":[49],"subtly":[50],"parameters,":[53],"which":[54],"reposition":[55],"system":[57],"after":[59],"spiking.":[60],"obtain":[62,82],"explicit":[63,103],"approximations":[64],"instantaneous":[66],"firing":[67,84],"rates":[68,85],"for":[69,105],"fixed":[70],"values":[71],"use":[77],"averaging":[79],"theorem":[80],"to":[81],"asymptotic":[83],"function":[88],"parameters.":[93],"Along":[94],"different":[97,109,118],"phase-plane":[98],"geometries,":[99],"these":[100],"computations":[101],"provide":[102],"tools":[104],"interpretation":[107],"spiking":[110],"patterns":[111],"guide":[113],"parameter":[114],"selection":[115],"in":[116],"modeling":[117],"cortical":[119],"cell":[120],"types.":[121]},"counts_by_year":[{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-01T08:55:55.761014","created_date":"2025-10-10T00:00:00"}