{"id":"https://openalex.org/W1998257686","doi":"https://doi.org/10.1137/s1111111102409882","title":"Bifurcation on the Visual Cortex with Weakly Anisotropic Lateral Coupling","display_name":"Bifurcation on the Visual Cortex with Weakly Anisotropic Lateral Coupling","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1998257686","doi":"https://doi.org/10.1137/s1111111102409882","mag":"1998257686"},"language":"en","primary_location":{"id":"doi:10.1137/s1111111102409882","doi":"https://doi.org/10.1137/s1111111102409882","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1111111102409882","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,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"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"},"volume":null,"type":"article","is_traditional":true,"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/A5044405191","display_name":"Martin Golubitsky","orcid":"https://orcid.org/0000-0002-6176-8756","observed_orcids":["https://orcid.org/0000-0002-6176-8756"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Golubitsky","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110048654","display_name":"Lie June Shiau","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lie June Shiau","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108471422","display_name":"Andrei T\u00f6r\u00f6k","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrei T\u00f6r\u00f6k","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"2","issue":"2","first_page":"97","last_page":"143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.7470999956130981,"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"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.7470999956130981,"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/T10581","display_name":"Neural dynamics and brain function","score":0.14820000529289246,"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/T13397","display_name":"Hallucinations in medical conditions","score":0.033399999141693115,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/primary-visual-cortex","display_name":"primary visual cortex","score":0.7429999709129333},{"id":"https://openalex.org/keywords/wilson-cowan-model","display_name":"Wilson-Cowan model","score":0.7990000247955322},{"id":"https://openalex.org/keywords/symmetry-breaking-bifurcation","display_name":"symmetry-breaking bifurcation","score":0.7599999904632568},{"id":"https://openalex.org/keywords/pattern-formation","display_name":"pattern formation","score":0.6890000104904175},{"id":"https://openalex.org/keywords/hypercolumns","display_name":"hypercolumns","score":0.6100000143051147},{"id":"https://openalex.org/keywords/orientation-tuning","display_name":"orientation tuning","score":0.9589999914169312},{"id":"https://openalex.org/keywords/drug-induced-hallucinations","display_name":"drug-induced hallucinations","score":0.7139999866485596},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.5460000038146973}],"concepts":[{"id":"https://openalex.org/C2779345533","wikidata":"https://www.wikidata.org/wiki/Q75785","display_name":"Visual cortex","level":2,"score":0.8124555349349976},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5682297945022583},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5573663115501404},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.5525878071784973},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.45455729961395264},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.44864141941070557},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.44622039794921875},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.43474462628364563},{"id":"https://openalex.org/C163931696","wikidata":"https://www.wikidata.org/wiki/Q7102406","display_name":"Orientation column","level":4,"score":0.42972031235694885},{"id":"https://openalex.org/C72064307","wikidata":"https://www.wikidata.org/wiki/Q1141237","display_name":"Lateral inhibition","level":2,"score":0.41345611214637756},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.36746180057525635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.264582097530365},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.19624537229537964},{"id":"https://openalex.org/C2993054123","wikidata":"https://www.wikidata.org/wiki/Q75785","display_name":"Striate cortex","level":3,"score":0.1826213300228119},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.17931166291236877},{"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1111111102409882","doi":"https://doi.org/10.1137/s1111111102409882","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1111111102409882","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,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"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:CiteSeerX.psu:10.1.1.221.3850","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.3850","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uh.edu/%7Etorok/Personal/papers/hallucinate.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1520835641","https://openalex.org/W1521230208","https://openalex.org/W1821468701","https://openalex.org/W1951259116","https://openalex.org/W1965778005","https://openalex.org/W1979506444","https://openalex.org/W1985475725","https://openalex.org/W1993980706","https://openalex.org/W2011764458","https://openalex.org/W2011937936","https://openalex.org/W2015931493","https://openalex.org/W2016354087","https://openalex.org/W2044072757","https://openalex.org/W2075721615","https://openalex.org/W2090286902","https://openalex.org/W2094930158","https://openalex.org/W2103510455","https://openalex.org/W2121881348","https://openalex.org/W2126430166","https://openalex.org/W2134831221","https://openalex.org/W2768464361","https://openalex.org/W4239981491"],"related_works":["https://openalex.org/W7097563000","https://openalex.org/W2163682865","https://openalex.org/W2143965680","https://openalex.org/W2121881348","https://openalex.org/W2117656921","https://openalex.org/W2134831221","https://openalex.org/W2131516772","https://openalex.org/W1484166894","https://openalex.org/W2014070605","https://openalex.org/W14669411"],"abstract_inverted_index":{"Mathematical":[0],"studies":[1],"of":[2,15,21,61,74,92,99,119,135,178,216,225,305,367,388,401,439,464,477,495,502],"drug":[3],"induced":[4],"geometric":[5,32],"visual":[6,24,48,218,466],"hallucinations":[7],"include":[8,95],"three":[9,437],"components:":[10],"a":[11,27,41,73,118,211,289,309,369,456,499],"model":[12,58,212,412,422,435,490],"(or":[13,453],"class":[14,91,501],"models)":[16],"that":[17,66,140,147,188,281,294,448,475],"abstracts":[18],"the":[19,22,37,54,59,70,75,96,104,115,120,123,161,168,173,176,202,217,223,227,242,257,319,334,348,407,418,462,465,492],"structure":[20],"primary":[23],"cortex":[25,174],"V1;":[26],"mathematical":[28],"procedure":[29],"for":[30,43,68],"finding":[31],"patterns":[33,46,295],"as":[34,47,252,368,445],"solutions":[35,282],"to":[36,57,94,130,160,213,230,272,288,302,377,450],"cortical":[38,265],"models;":[39],"and":[40,51,87,103,106,128,164,207,248,254,256,293,415,431,468],"method":[42],"interpreting":[44],"these":[45,110,240,389],"hallucinations.":[49],"Ermentrout":[50],"Cowan":[52],"used":[53],"Wilson--Cowan":[55],"equations":[56],"evolution":[60],"an":[62,357],"activity":[63],"variable":[64],"a(x)":[65],"represents,":[67],"example,":[69],"voltage":[71,116],"potential":[72,117],"neuron":[76,121],"located":[77,125],"at":[78,126],"point":[79],"x":[80,127,344],"in":[81,101,122,150,172,194,239,324,333,379,386,406,424,461,485,498],"V1.":[82],"Bressloff,":[83],"Cowan,":[84],"Golubitsky,":[85],"Thomas,":[86],"Wiener":[88],"generalize":[89],"this":[90,183,489,496],"models":[93,243,246,258],"orientation":[97,163,204],"tuning":[98],"neurons":[100,149,169,193],"V1":[102],"Hubel":[105],"Wiesel":[107],"hypercolumns.":[108],"In":[109,182,318,351],"models,":[111],"$a({\\mathbf":[112],"x},\\phi)$":[113],"represents":[114],"hypercolumn":[124],"tuned":[129,159],"direction":[131,177],"$\\phi$.":[132],"The":[133,270,383,410],"work":[134],"Bressloff":[136,335,419],"et":[137,336,420],"al.":[138,337,421],"assumes":[139],"lateral":[141,189,228,266],"connections":[142,190],"between":[143],"hypercolumns":[144,152,196,249],"are":[145,153,158,170,191,197,235,244,250,268,283,296,314],"anisotropic;":[146],"is,":[148],"neighboring":[151,195],"connected":[154,198],"only":[155,166],"if":[156,167],"they":[157,200],"same":[162,203],"then":[165,365],"oriented":[171],"along":[175,392],"their":[179],"cells'":[180],"preference.":[181],"work,":[184],"we":[185,221],"first":[186,493],"assume":[187],"isotropic:":[192],"whenever":[199],"have":[201,260,403],"tuning.":[205],"Wolf":[206],"Geisel":[208],"use":[209],"such":[210,444],"study":[214],"development":[215],"cortex.":[219],"Then":[220],"consider":[222],"effect":[224],"perturbing":[226],"couplings":[229],"be":[231],"weakly":[232],"anisotropic.":[233],"There":[234,313],"two":[236],"common":[237],"features":[238],"models:":[241],"continuum":[245],"(neurons":[247],"idealized":[251],"points":[253],"circles),":[255],"all":[259],"planar":[261,291],"Euclidean":[262],"E(2)-symmetry":[263],"(when":[264],"boundaries":[267],"ignored).":[269],"approach":[271],"pattern":[273],"formation":[274],"is":[275,279,364,473],"also":[276,315],"common.":[277],"It":[278],"assumed":[280],"spatially":[284,310],"periodic":[285],"with":[286,458,487],"respect":[287],"fixed":[290],"lattice":[292],"formed":[297],"by":[298],"symmetry-breaking":[299,372],"bifurcations":[300,484],"(corresponding":[301],"wave":[303],"vectors":[304],"shortest":[306],"length)":[307],"from":[308,373,482],"uniform":[311],"state.":[312],"substantial":[316],"differences.":[317],"Ermentrout--Cowan":[320,411],"model,":[321,338,353],"E(2)":[322,339,378],"acts":[323,340],"its":[325,380,459],"standard":[326],"representation":[327],"on":[328,341],"R":[329,342],"2":[330,343],",":[331],"whereas":[332,417],"S":[345,359,375],"1":[346,360,376],"via":[347],"shift-twist":[349,381],"action.":[350,382],"our":[352,434],"isotropic":[354],"coupling":[355],"introduces":[356],"additional":[358],"-symmetry.":[361],"Weak":[362],"anisotropy":[363],"thought":[366],"small":[370],"forced":[371],"E(2)\\dot{+}":[374],"bifurcation":[384],"analyses":[385],"each":[387,396],"theories":[390],"proceed":[391],"similar":[393],"lines,":[394],"but":[395],"produces":[397,413,423,436],"different":[398],"hallucinatory":[399],"images---many":[400],"which":[402],"been":[404],"reported":[405],"psychophysics":[408],"literature.":[409],"spirals":[414],"funnels,":[416],"addition":[425],"thin":[426],"line":[427],"images":[428],"including":[429],"honeycombs":[430],"cobwebs.":[432],"Finally,":[433],"types":[438],"time-periodic":[440,478],"states:":[441],"rotating":[442],"structures":[443],"spirals,":[446],"states":[447,479],"appear":[449],"rush":[451],"into":[452],"out":[454],"from)":[455],"tunnel":[457],"hole":[460],"center":[463],"field,":[467],"pulsating":[469],"images.":[470],"Although":[471],"it":[472],"known":[474],"branches":[476],"can":[480],"emanate":[481],"steady-state":[483],"systems":[486],"symmetry,":[488],"provides":[491],"examples":[494],"phenomena":[497],"specific":[500],"models.":[503]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
