{"id":"https://openalex.org/W2079804658","doi":"https://doi.org/10.1137/110858392","title":"Reduction and Dynamics of a Generalized Rivalry Network with Two Learned Patterns","display_name":"Reduction and Dynamics of a Generalized Rivalry Network with Two Learned Patterns","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2079804658","doi":"https://doi.org/10.1137/110858392","mag":"2079804658"},"language":"en","primary_location":{"id":"doi:10.1137/110858392","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110858392","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/A5063637873","display_name":"Casey O. Diekman","orcid":"https://orcid.org/0000-0002-4711-1395"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Casey Diekman","raw_affiliation_strings":["Ohio State University"],"affiliations":[{"raw_affiliation_string":"Ohio State University","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044405191","display_name":"Martin Golubitsky","orcid":"https://orcid.org/0000-0002-6176-8756"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Martin Golubitsky","raw_affiliation_strings":["Ohio State University"],"affiliations":[{"raw_affiliation_string":"Ohio State University","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057780637","display_name":"Tyler McMillen","orcid":null},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tyler McMillen","raw_affiliation_strings":["Ohio State University"],"affiliations":[{"raw_affiliation_string":"Ohio State University","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013723275","display_name":"Yunjiao Wang","orcid":"https://orcid.org/0000-0002-7002-0889"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yunjiao Wang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063637873"],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":0.558,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.6516114,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"11","issue":"4","first_page":"1270","last_page":"1309"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9987000226974487,"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":0.9987000226974487,"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/T10427","display_name":"Visual perception and processing mechanisms","score":0.9973999857902527,"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":0.9883000254631042,"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/rivalry","display_name":"Rivalry","score":0.669914186000824},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5701946020126343},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5065094232559204},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.48651260137557983},{"id":"https://openalex.org/keywords/multistability","display_name":"Multistability","score":0.45597517490386963},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.44125044345855713},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43926459550857544},{"id":"https://openalex.org/keywords/network-dynamics","display_name":"Network dynamics","score":0.43886998295783997},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.4348514974117279},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.431476354598999},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4010331630706787},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2361227571964264},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1935211420059204},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.15837407112121582},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10669031739234924},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0930967926979065},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08667248487472534}],"concepts":[{"id":"https://openalex.org/C2779602485","wikidata":"https://www.wikidata.org/wiki/Q2901966","display_name":"Rivalry","level":2,"score":0.669914186000824},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5701946020126343},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5065094232559204},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.48651260137557983},{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.45597517490386963},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.44125044345855713},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43926459550857544},{"id":"https://openalex.org/C123757187","wikidata":"https://www.wikidata.org/wiki/Q9195957","display_name":"Network dynamics","level":2,"score":0.43886998295783997},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.4348514974117279},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.431476354598999},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4010331630706787},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2361227571964264},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1935211420059204},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.15837407112121582},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10669031739234924},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0930967926979065},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08667248487472534},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110858392","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110858392","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W630730503","https://openalex.org/W1511383046","https://openalex.org/W1964726990","https://openalex.org/W1965259272","https://openalex.org/W1965503267","https://openalex.org/W1965778005","https://openalex.org/W1969836308","https://openalex.org/W1986652999","https://openalex.org/W1988507461","https://openalex.org/W2015558818","https://openalex.org/W2029899509","https://openalex.org/W2036519091","https://openalex.org/W2044100433","https://openalex.org/W2045968318","https://openalex.org/W2054290723","https://openalex.org/W2064608742","https://openalex.org/W2087205232","https://openalex.org/W2089876099","https://openalex.org/W2101848767","https://openalex.org/W2107062755","https://openalex.org/W2129270652","https://openalex.org/W2130069331","https://openalex.org/W2132323186","https://openalex.org/W2140583928","https://openalex.org/W2157641779","https://openalex.org/W2160229024","https://openalex.org/W2161967412","https://openalex.org/W2164173137","https://openalex.org/W2165092209","https://openalex.org/W2168480378","https://openalex.org/W2169469537","https://openalex.org/W2480701976","https://openalex.org/W2487249630","https://openalex.org/W2495006976","https://openalex.org/W4206135370","https://openalex.org/W4211057129","https://openalex.org/W4241364206"],"related_works":["https://openalex.org/W1527571384","https://openalex.org/W2383189914","https://openalex.org/W4301445084","https://openalex.org/W2963840034","https://openalex.org/W1984975294","https://openalex.org/W4226178663","https://openalex.org/W1517717759","https://openalex.org/W1964251919","https://openalex.org/W4241282949","https://openalex.org/W2316579689"],"abstract_inverted_index":{"We":[0,21,106,134,171],"use":[1],"the":[2,24,61,91,96,100,116,128,136,139,143,150,155,165,168,175,182,186,189],"theory":[3],"of":[4,26,38,51,78,127,138,149,167],"coupled":[5],"cell":[6],"systems":[7,141],"to":[8,47,74,86,123,130,160],"analyze":[9,135],"a":[10,48,131,161],"neuronal":[11],"network":[12,93,102,176],"model":[13,49],"for":[14,188],"generalized":[15],"rivalry":[16,27],"posed":[17],"by":[18],"H.":[19],"Wilson.":[20],"focus":[22],"on":[23,57],"case":[25],"between":[28],"two":[29,52],"patterns":[30,62],"and":[31,41,119,185],"identify":[32],"conditions":[33],"under":[34],"which":[35],"large":[36,87],"networks":[37],"$n$":[39],"attributes":[40],"$m$":[42],"intensity":[43],"levels":[44,66],"can":[45,84],"reduce":[46,125],"consisting":[50],"or":[53,59],"three":[54],"cells":[55,98],"depending":[56],"whether":[58],"not":[60],"have":[63,104],"any":[64],"attribute":[65],"in":[67,90,99,115,181],"common.":[68],"(The":[69],"two-cell":[70],"reduction":[71],"is":[72,194],"equivalent":[73],"certain":[75],"recent":[76],"models":[77],"binocular":[79],"rivalry.)":[80],"Notably,":[81],"these":[82],"reductions":[83],"lead":[85],"recurrent":[88,179],"excitation":[89,180],"reduced":[92,117,183],"even":[94],"though":[95],"individual":[97],"original":[101],"may":[103],"none.":[105],"also":[107,172],"show":[108],"that":[109],"symmetry-breaking":[110],"Takens--Bogdanov":[111],"(TB)":[112],"bifurcations":[113],"occur":[114],"networks,":[118,184],"this":[120],"allows":[121],"us":[122],"further":[124],"much":[126],"dynamics":[129,137],"planar":[132],"system.":[133],"quotient":[140],"near":[142],"TB":[144,169],"singularity,":[145],"discussing":[146],"how":[147,174],"variation":[148,158],"input":[151],"parameter":[152],"$I$":[153],"organizes":[154],"dynamics.":[156,190],"This":[157],"leads":[159],"degenerate":[162],"path":[163],"through":[164],"unfolding":[166],"point.":[170],"discuss":[173],"structure":[177],"affects":[178],"consequences":[187],"(A":[191],"corrected":[192],"PDF":[193],"attached.)":[195]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
