{"id":"https://openalex.org/W2025973190","doi":"https://doi.org/10.1137/s0036144500382064","title":"Synchronization of Elliptic Bursters","display_name":"Synchronization of Elliptic Bursters","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2025973190","doi":"https://doi.org/10.1137/s0036144500382064","mag":"2025973190"},"language":"en","primary_location":{"id":"doi:10.1137/s0036144500382064","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144500382064","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5091804814","display_name":"Eugene M. Izhikevich","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Eugene M. Izhikevich","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091804814"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.79628482,"has_fulltext":false,"cited_by_count":166,"citation_normalized_percentile":{"value":0.89191501,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"43","issue":"2","first_page":"315","last_page":"344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9997000098228455,"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":0.9997000098228455,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9997000098228455,"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"}},{"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bursting","display_name":"Bursting","score":0.734312117099762},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.6432544589042664},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5684918165206909},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5516008734703064},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.5508711338043213},{"id":"https://openalex.org/keywords/relaxation-oscillator","display_name":"Relaxation oscillator","score":0.5478132367134094},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5343664288520813},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4988667964935303},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.421374648809433},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37902480363845825},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3472130298614502},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3342432379722595},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.31238865852355957},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2825651168823242},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2515239715576172},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.2008504867553711},{"id":"https://openalex.org/keywords/neuroscience","display_name":"Neuroscience","score":0.18125852942466736},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15288004279136658},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12743186950683594},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09119528532028198},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0866653323173523},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.0797644555568695}],"concepts":[{"id":"https://openalex.org/C195221683","wikidata":"https://www.wikidata.org/wiki/Q5000649","display_name":"Bursting","level":2,"score":0.734312117099762},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6432544589042664},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5684918165206909},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5516008734703064},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.5508711338043213},{"id":"https://openalex.org/C135854075","wikidata":"https://www.wikidata.org/wiki/Q1421688","display_name":"Relaxation oscillator","level":4,"score":0.5478132367134094},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5343664288520813},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4988667964935303},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.421374648809433},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37902480363845825},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3472130298614502},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3342432379722595},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.31238865852355957},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2825651168823242},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2515239715576172},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2008504867553711},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.18125852942466736},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15288004279136658},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12743186950683594},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09119528532028198},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0866653323173523},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0797644555568695},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C5291336","wikidata":"https://www.wikidata.org/wiki/Q852341","display_name":"Voltage-controlled oscillator","level":3,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036144500382064","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144500382064","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W54326250","https://openalex.org/W84463169","https://openalex.org/W1491439616","https://openalex.org/W1560335986","https://openalex.org/W1596321532","https://openalex.org/W1964294610","https://openalex.org/W1965259272","https://openalex.org/W1971657654","https://openalex.org/W1985940938","https://openalex.org/W1988934258","https://openalex.org/W2007433796","https://openalex.org/W2009375605","https://openalex.org/W2025604508","https://openalex.org/W2027503001","https://openalex.org/W2031063322","https://openalex.org/W2042941790","https://openalex.org/W2046424015","https://openalex.org/W2050162047","https://openalex.org/W2064108635","https://openalex.org/W2072413244","https://openalex.org/W2072494173","https://openalex.org/W2079173805","https://openalex.org/W2080018957","https://openalex.org/W2105714117","https://openalex.org/W2110586973","https://openalex.org/W2113239165","https://openalex.org/W2116829706","https://openalex.org/W2119443761","https://openalex.org/W2145296723","https://openalex.org/W2149525340","https://openalex.org/W2198725279","https://openalex.org/W2404697796","https://openalex.org/W2419220035","https://openalex.org/W2484910965","https://openalex.org/W4206651839","https://openalex.org/W4254773097"],"related_works":["https://openalex.org/W4296292881","https://openalex.org/W3197610365","https://openalex.org/W2115351049","https://openalex.org/W2353430195","https://openalex.org/W1987359200","https://openalex.org/W178781247","https://openalex.org/W2094768441","https://openalex.org/W4206634936","https://openalex.org/W2045360568","https://openalex.org/W2364054655"],"abstract_inverted_index":{"Periodic":[0],"bursting":[1],"behavior":[2,74,83],"in":[3],"neurons":[4],"is":[5,43,78,113],"a":[6,10,24,53,98],"recurrent":[7],"transition":[8,18,30],"between":[9,127],"quiescent":[11,33],"state":[12,34],"and":[13,28,89,111,158],"repetitive":[14,20],"spiking.":[15],"When":[16],"the":[17,29,32,41,60,73,82,132,136,142,147,155],"to":[19,31,45,109,161],"spiking":[21,133],"occurs":[22,35],"via":[23,36],"subcritical":[25],"Andronov--Hopf":[26],"bifurcation":[27],"fold":[37],"limit":[38],"cycle":[39],"bifurcation,":[40],"burster":[42],"said":[44],"be":[46],"of":[47,63,67,75,84,92,149],"elliptic":[48],"type":[49],"(also":[50],"known":[51],"as":[52],"\"subHopf/fold":[54],"cycle\"":[55],"burster).":[56],"Here":[57],"we":[58,153],"study":[59],"synchronization":[61,112],"dynamics":[62],"weakly":[64,85,101],"connected":[65,86,94,102],"networks":[66,77],"such":[68,76,100],"bursters.":[69],"We":[70,122],"find":[71,124],"that":[72,91,125],"quite":[79,118],"different":[80,119],"from":[81],"phase":[87],"oscillators":[88],"resembles":[90],"strongly":[93],"relaxation":[95],"oscillators.":[96],"As":[97],"result,":[99],"bursters":[103,116,128],"need":[104],"few":[105],"(usually":[106],"one)":[107],"bursts":[108],"synchronize,":[110],"possible":[114],"for":[115],"having":[117],"quantitative":[120],"features.":[121],"also":[123],"interactions":[126,137],"depend":[129],"crucially":[130],"on":[131],"frequencies.":[134],"Namely,":[135],"are":[138],"most":[139],"effective":[140],"when":[141],"presynaptic":[143],"interspike":[144],"frequency":[145,148],"matches":[146],"postsynaptic":[150],"oscillations.":[151],"Finally,":[152],"use":[154],"FitzHugh--Rinzel,":[156],"Morris--Lecar,":[157],"Hodgkin--Huxley":[159],"models":[160],"illustrate":[162],"our":[163],"major":[164],"results.":[165]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":11}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}