{"id":"https://openalex.org/W2062037720","doi":"https://doi.org/10.1137/10081811x","title":"A Contraction Argument for Two-Dimensional Spiking Neuron Models","display_name":"A Contraction Argument for Two-Dimensional Spiking Neuron Models","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2062037720","doi":"https://doi.org/10.1137/10081811x","mag":"2062037720"},"language":"en","primary_location":{"id":"doi:10.1137/10081811x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/10081811x","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/A5015061477","display_name":"Eric Foxall","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eric Foxall","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056190390","display_name":"Roderick Edwards","orcid":"https://orcid.org/0000-0002-8239-5987"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roderick Edwards","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086564918","display_name":"Slim Ibrahim","orcid":"https://orcid.org/0000-0002-5072-8062"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Slim Ibrahim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049802779","display_name":"P. van den Driessche","orcid":"https://orcid.org/0000-0003-1485-8326"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. van den Driessche","raw_affiliation_strings":["(Department of Mathematics and Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(Department of Mathematics and Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4264,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.69381749,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"1","first_page":"540","last_page":"566"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9998000264167786,"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":0.9991000294685364,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/biological-neuron-model","display_name":"Biological neuron model","score":0.5788841247558594},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5357721447944641},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.531814694404602},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5188142657279968},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.5080220699310303},{"id":"https://openalex.org/keywords/reset","display_name":"Reset (finance)","score":0.48740914463996887},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4797700345516205},{"id":"https://openalex.org/keywords/phase-plane","display_name":"Phase plane","score":0.4772603213787079},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.4705900251865387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39092332124710083},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2179412841796875},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18771260976791382},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15045350790023804},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12395203113555908},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.07961085438728333},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.07583406567573547}],"concepts":[{"id":"https://openalex.org/C186565885","wikidata":"https://www.wikidata.org/wiki/Q1651163","display_name":"Biological neuron model","level":3,"score":0.5788841247558594},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5357721447944641},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.531814694404602},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5188142657279968},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5080220699310303},{"id":"https://openalex.org/C2779795794","wikidata":"https://www.wikidata.org/wiki/Q7315343","display_name":"Reset (finance)","level":2,"score":0.48740914463996887},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4797700345516205},{"id":"https://openalex.org/C157626765","wikidata":"https://www.wikidata.org/wiki/Q2088081","display_name":"Phase plane","level":3,"score":0.4772603213787079},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.4705900251865387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39092332124710083},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2179412841796875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18771260976791382},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15045350790023804},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12395203113555908},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.07961085438728333},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.07583406567573547},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","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/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/10081811x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/10081811x","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:dspace.library.uvic.ca:1828/3459","is_oa":false,"landing_page_url":"http://hdl.handle.net/1828/3459","pdf_url":null,"source":{"id":"https://openalex.org/S4306401509","display_name":"UVic\u2019s Research and Learning Repository (University of Victoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I212119943","host_organization_name":"University of Victoria","host_organization_lineage":["https://openalex.org/I212119943"],"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":"Thesis"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W316919195","https://openalex.org/W1576838367","https://openalex.org/W1983069678","https://openalex.org/W1985940938","https://openalex.org/W1990321067","https://openalex.org/W1997576506","https://openalex.org/W2009375605","https://openalex.org/W2029342452","https://openalex.org/W2029924743","https://openalex.org/W2058479255","https://openalex.org/W2091144817","https://openalex.org/W2091960773","https://openalex.org/W2096430020","https://openalex.org/W2097415784","https://openalex.org/W2101793659","https://openalex.org/W2128949090","https://openalex.org/W2134889984","https://openalex.org/W2154959070","https://openalex.org/W2157102451","https://openalex.org/W2164653071","https://openalex.org/W3141151088","https://openalex.org/W3150827945","https://openalex.org/W3217350819"],"related_works":["https://openalex.org/W350273603","https://openalex.org/W2393495588","https://openalex.org/W96259911","https://openalex.org/W2168225754","https://openalex.org/W4385608460","https://openalex.org/W2185689080","https://openalex.org/W4285239028","https://openalex.org/W1977018762","https://openalex.org/W2579997181","https://openalex.org/W2144751034"],"abstract_inverted_index":{"A":[0],"number":[1],"of":[2,25,29,39,46,50,71],"two-dimensional":[3],"spiking":[4,32,66,100,122],"neuron":[5],"models":[6,22,82],"that":[7,120],"combine":[8],"continuous":[9],"dynamics":[10],"with":[11],"an":[12,44],"instantaneous":[13],"reset":[14],"have":[15,36],"been":[16],"introduced":[17],"in":[18,52,83],"the":[19,37,47,53,61,84,88,92,104],"literature.":[20,86],"The":[21,69],"are":[23,108,116],"capable":[24],"reproducing":[26],"a":[27],"variety":[28],"experimentally":[30],"observed":[31],"patterns":[33],"and":[34,98,111],"also":[35],"advantage":[38],"being":[40],"mathematically":[41],"tractable.":[42],"Here":[43],"analysis":[45],"transverse":[48],"stability":[49],"orbits":[51],"phase":[54],"plane":[55],"leads":[56],"to":[57,67,118],"sufficient":[58],"conditions":[59],"on":[60],"model":[62,93],"parameters":[63],"for":[64],"regular":[65,99,121],"occur.":[68],"application":[70],"this":[72],"method":[73],"is":[74],"illustrated":[75],"by":[76],"three":[77],"examples,":[78],"taken":[79],"from":[80],"existing":[81],"neuroscience":[85],"In":[87,103],"first":[89],"two":[90],"examples":[91],"has":[94],"no":[95],"equilibrium":[96,109],"states,":[97],"follows":[101],"directly.":[102],"third":[105],"example":[106],"there":[107],"points,":[110],"some":[112],"additional":[113],"quantitative":[114],"arguments":[115],"given":[117],"prove":[119],"occurs.":[123]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}
