{"id":"https://openalex.org/W2105809413","doi":"https://doi.org/10.1142/s0218127407018919","title":"GLOBAL CONSISTENCY OF DECISIONS AND CONVERGENCE OF COMPETITIVE CELLULAR NEURAL NETWORKS","display_name":"GLOBAL CONSISTENCY OF DECISIONS AND CONVERGENCE OF COMPETITIVE CELLULAR NEURAL NETWORKS","publication_year":2007,"publication_date":"2007-09-01","ids":{"openalex":"https://openalex.org/W2105809413","doi":"https://doi.org/10.1142/s0218127407018919","mag":"2105809413"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127407018919","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407018919","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5080374992","display_name":"Mauro Di Marco","orcid":"https://orcid.org/0000-0002-0013-9112"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"M. DI MARCO","raw_affiliation_strings":["Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, v. Roma 56 \u2014 53100 Siena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, v. Roma 56 \u2014 53100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069809502","display_name":"Mauro Forti","orcid":"https://orcid.org/0000-0002-3970-7201"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"M. FORTI","raw_affiliation_strings":["Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, v. Roma 56 \u2014 53100 Siena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, v. Roma 56 \u2014 53100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064424150","display_name":"Massimiliano Grazzini","orcid":"https://orcid.org/0000-0002-3143-7331"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"M. GRAZZINI","raw_affiliation_strings":["Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, v. Roma 56 \u2014 53100 Siena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, v. Roma 56 \u2014 53100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064881566","display_name":"Paolo Nistri","orcid":"https://orcid.org/0000-0001-6643-4600"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"P. NISTRI","raw_affiliation_strings":["Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, v. Roma 56 \u2014 53100 Siena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, v. Roma 56 \u2014 53100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003092391","display_name":"Luca Pancioni","orcid":"https://orcid.org/0000-0002-2502-9542"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"L. PANCIONI","raw_affiliation_strings":["Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, v. Roma 56 \u2014 53100 Siena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, v. Roma 56 \u2014 53100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5080374992"],"corresponding_institution_ids":["https://openalex.org/I102064193"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.15500735,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"17","issue":"09","first_page":"3127","last_page":"3150"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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":0.9829000234603882,"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":0.979200005531311,"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/convergence","display_name":"Convergence (economics)","score":0.6287420392036438},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5495872497558594},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4828275144100189},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.48038536310195923},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4714554250240326},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4664810299873352},{"id":"https://openalex.org/keywords/uniform-convergence","display_name":"Uniform convergence","score":0.4584251642227173},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.45577454566955566},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4525711238384247},{"id":"https://openalex.org/keywords/cellular-neural-network","display_name":"Cellular neural network","score":0.4316927492618561},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4247701168060303},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4103727340698242},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.41029077768325806},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32150185108184814},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21317586302757263},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1860204041004181},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.11469888687133789},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08206304907798767},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.07439491152763367}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6287420392036438},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5495872497558594},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4828275144100189},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.48038536310195923},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4714554250240326},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4664810299873352},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.4584251642227173},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.45577454566955566},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4525711238384247},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.4316927492618561},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4247701168060303},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4103727340698242},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.41029077768325806},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32150185108184814},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21317586302757263},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1860204041004181},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.11469888687133789},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08206304907798767},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.07439491152763367},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127407018919","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407018919","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:usiena-air.unisi.it:11365/24665","is_oa":false,"landing_page_url":"http://hdl.handle.net/11365/24665","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7699999809265137,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1502414959","https://openalex.org/W1514578360","https://openalex.org/W1971529282","https://openalex.org/W1996534584","https://openalex.org/W1996773027","https://openalex.org/W2025221203","https://openalex.org/W2030533255","https://openalex.org/W2062194437","https://openalex.org/W2066263844","https://openalex.org/W2109218509","https://openalex.org/W2124619121","https://openalex.org/W2135892798","https://openalex.org/W2137316616","https://openalex.org/W2139145615","https://openalex.org/W2143520356","https://openalex.org/W2160121923","https://openalex.org/W4210718478"],"related_works":["https://openalex.org/W2012452884","https://openalex.org/W2089309623","https://openalex.org/W2352053904","https://openalex.org/W2560976079","https://openalex.org/W2384469913","https://openalex.org/W2375782781","https://openalex.org/W2942509622","https://openalex.org/W4286986829","https://openalex.org/W2087820718","https://openalex.org/W130791004"],"abstract_inverted_index":{"In":[0,71],"a":[1,12,25,44,104,144,173,186,241,266],"series":[2],"of":[3,24,27,58,64,82,125,143,169,175,177,236,248,251,269,272,286],"papers":[4],"published":[5],"in":[6,51,154,281],"the":[7,17,36,59,74,80,97,100,118,123,126,135,141,155,159,170,222,233,249,262],"seventies,":[8],"Grossberg":[9,75],"had":[10],"developed":[11],"geometric":[13],"approach":[14,32,76,137],"for":[15,200],"analyzing":[16],"global":[18,56,195,270],"dynamical":[19,29,253],"behavior":[20],"and":[21,54,89,113,191,197,209,246],"convergence":[22,63,95,153,198,234,285],"properties":[23,235],"class":[26,81,250],"competitive":[28,49,83,101,180,237,252,287],"systems.":[30],"The":[31,109,216],"is":[33,40,77,91,111,131,149,224],"based":[34],"on":[35],"property":[37],"that":[38,52,55,99,134,220,277],"it":[39,90,148],"possible":[41],"to":[42,79,93,115,151,204,261,264,276,283],"associate":[43],"decision":[45,60,107,189,244],"scheme":[46,61,190],"with":[47,117,206,274,289],"each":[48,65],"system":[50],"class,":[53],"consistency":[57,196,271],"implies":[62],"solution":[66],"toward":[67],"some":[68],"stationary":[69],"state.":[70],"this":[72],"paper,":[73],"extended":[78,136,171],"standard":[84],"Cellular":[85],"Neural":[86],"Networks":[87],"(CNNs),":[88],"used":[92],"investigate":[94],"under":[96],"hypothesis":[98],"CNN":[102,127,160],"has":[103],"globally":[105,187,242],"consistent":[106,188,243],"scheme.":[108],"extension":[110],"nonobvious":[112],"requires":[114],"deal":[116],"set-valued":[119],"vector":[120],"field":[121],"describing":[122],"dynamics":[124],"output":[128],"solutions.":[129],"It":[130],"also":[132,218],"stressed":[133],"does":[138],"not":[139,164],"require":[140],"existence":[142],"Lyapunov":[145],"function,":[146],"hence":[147],"applicable":[150],"address":[152],"general":[156],"case":[157],"where":[158],"neuron":[161],"interconnections":[162],"are":[163,182,192,229],"necessarily":[165],"symmetric.":[166],"By":[167],"means":[168],"approach,":[172],"number":[174],"classes":[176],"third-order":[178],"nonsymmetric":[179],"CNNs":[181,238,288],"discovered,":[183],"which":[184],"have":[185],"convergent.":[193],"Moreover,":[194],"hold":[199],"interconnection":[201],"parameters":[202],"belonging":[203],"sets":[205],"non-empty":[207],"interior,":[208],"thus":[210],"they":[211],"represent":[212],"physically":[213],"robust":[214],"properties.":[215],"paper":[217],"shows":[219],"when":[221],"dimension":[223],"higher":[225],"than":[226,291],"three,":[227],"there":[228],"fundamental":[230],"differences":[231,259],"between":[232],"implied":[239],"by":[240,256,279],"scheme,":[245],"those":[247],"systems":[254],"considered":[255],"Grossberg.":[257],"These":[258],"lead":[260],"need":[263],"introduce":[265],"stronger":[267],"notion":[268],"decisions,":[273],"respect":[275],"proposed":[278],"Grossberg,":[280],"order":[282],"guarantee":[284],"more":[290],"three":[292],"neurons.":[293]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}