{"id":"https://openalex.org/W4290995040","doi":"https://doi.org/10.1109/tcsi.2022.3194465","title":"Edge of Chaos Is Sine Qua Non for Turing Instability","display_name":"Edge of Chaos Is Sine Qua Non for Turing Instability","publication_year":2022,"publication_date":"2022-08-11","ids":{"openalex":"https://openalex.org/W4290995040","doi":"https://doi.org/10.1109/tcsi.2022.3194465"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2022.3194465","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2022.3194465","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","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/A5023152110","display_name":"Alon Ascoli","orcid":"https://orcid.org/0000-0003-4026-9648"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alon Ascoli","raw_affiliation_strings":["Faculty of Electrical and Computer Engineering, Institute of Circuits and Systems, Technische Universit&#x00E4;t Dresden, Dresden, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Electrical and Computer Engineering, Institute of Circuits and Systems, Technische Universit&#x00E4;t Dresden, Dresden, Germany","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066450151","display_name":"Ahmet \u015eamil Demirkol","orcid":"https://orcid.org/0000-0002-1236-1300"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ahmet Samil Demirkol","raw_affiliation_strings":["Faculty of Electrical and Computer Engineering, Institute of Circuits and Systems, Technische Universit&#x00E4;t Dresden, Dresden, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Electrical and Computer Engineering, Institute of Circuits and Systems, Technische Universit&#x00E4;t Dresden, Dresden, Germany","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012451668","display_name":"Ronald Tetzlaff","orcid":"https://orcid.org/0000-0001-7436-0103"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ronald Tetzlaff","raw_affiliation_strings":["Faculty of Electrical and Computer Engineering, Institute of Circuits and Systems, Technische Universit&#x00E4;t Dresden, Dresden, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Electrical and Computer Engineering, Institute of Circuits and Systems, Technische Universit&#x00E4;t Dresden, Dresden, Germany","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090657067","display_name":"Leon O. Chua","orcid":"https://orcid.org/0000-0002-1652-5464"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leon Chua","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5023152110"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2359,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.94971581,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"69","issue":"11","first_page":"4596","last_page":"4609"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":1.0,"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":1.0,"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":0.9993000030517578,"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":0.998199999332428,"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/edge-of-chaos","display_name":"Edge of chaos","score":0.6707152724266052},{"id":"https://openalex.org/keywords/memristor","display_name":"Memristor","score":0.6467472314834595},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.6398017406463623},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5635350942611694},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4749698340892792},{"id":"https://openalex.org/keywords/cellular-neural-network","display_name":"Cellular neural network","score":0.431199848651886},{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.42042461037635803},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.41064274311065674},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.40561243891716003},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4029940366744995},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.32254642248153687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24554443359375},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.20281684398651123},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.17790290713310242},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16189807653427124},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15936529636383057},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14405474066734314},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13009455800056458}],"concepts":[{"id":"https://openalex.org/C2780713532","wikidata":"https://www.wikidata.org/wiki/Q93158","display_name":"Edge of chaos","level":2,"score":0.6707152724266052},{"id":"https://openalex.org/C150072547","wikidata":"https://www.wikidata.org/wiki/Q212923","display_name":"Memristor","level":2,"score":0.6467472314834595},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.6398017406463623},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5635350942611694},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4749698340892792},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.431199848651886},{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.42042461037635803},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.41064274311065674},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40561243891716003},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4029940366744995},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.32254642248153687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24554443359375},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.20281684398651123},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.17790290713310242},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16189807653427124},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15936529636383057},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14405474066734314},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13009455800056458},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2022.3194465","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2022.3194465","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","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":32,"referenced_works":["https://openalex.org/W1606202192","https://openalex.org/W1972963245","https://openalex.org/W1975229527","https://openalex.org/W1975647260","https://openalex.org/W1980661496","https://openalex.org/W1993214330","https://openalex.org/W2018341541","https://openalex.org/W2019061854","https://openalex.org/W2026913344","https://openalex.org/W2030834420","https://openalex.org/W2054648042","https://openalex.org/W2312610232","https://openalex.org/W2500183209","https://openalex.org/W2755163763","https://openalex.org/W2788512397","https://openalex.org/W2891281574","https://openalex.org/W2900178210","https://openalex.org/W3099086962","https://openalex.org/W3101667202","https://openalex.org/W3135101291","https://openalex.org/W3156265125","https://openalex.org/W3198585701","https://openalex.org/W3217786002","https://openalex.org/W4207006543","https://openalex.org/W4210689979","https://openalex.org/W4213100547","https://openalex.org/W4241546294","https://openalex.org/W4288058162","https://openalex.org/W4292745312","https://openalex.org/W4310301864","https://openalex.org/W4310873083","https://openalex.org/W4312081754"],"related_works":["https://openalex.org/W2770598252","https://openalex.org/W2805246418","https://openalex.org/W4288917018","https://openalex.org/W3021750181","https://openalex.org/W2052888871","https://openalex.org/W2582906043","https://openalex.org/W4301628837","https://openalex.org/W3022993598","https://openalex.org/W1973200562","https://openalex.org/W1981364541"],"abstract_inverted_index":{"Diffusion-driven":[0],"instabilities":[1,71],"with":[2,72,90,181],"pattern":[3],"formation":[4],"may":[5,177],"occur":[6],"in":[7,32,107,123],"a":[8,26,159,174],"network":[9],"of":[10,35,76,118,142,168],"identical,":[11],"regularly-spaced,":[12],"and":[13,17,28,58,67,129,148,154,165],"resistively-coupled":[14],"cells":[15],"if":[16,19,128,131],"only":[18,49,130],"the":[20,33,41,73,83,100,119,132,140,163,169],"uncoupled":[21,133],"cell":[22,134],"is":[23,82,110],"poised":[24],"on":[25],"locally-active":[27,97],"stable":[29],"operating":[30],"point":[31],"Edge":[34,141],"Chaos":[36,143],"domain.":[37,144],"This":[38],"manuscript":[39],"presents":[40],"simplest":[42],"ever-reported":[43],"two-cell":[44,126],"neural":[45],"network,":[46,171],"combining":[47],"together":[48],"7":[50],"two-terminal":[51],"components,":[52],"namely":[53],"2":[54,59,96],"batteries,":[55],"3":[56],"resistors,":[57],"volatile":[60],"NbOx":[61],"memristive":[62,184],"threshold":[63],"switches":[64],"from":[65,139],"NaMLab,":[66],"subject":[68],"to":[69,104,112],"diffusion-driven":[70],"concurrent":[74],"emergence":[75],"Turing":[77],"patterns.":[78],"Very":[79],"remarkably,":[80],"this":[81,108,124],"first":[84],"time":[85],"an":[86],"homogeneous":[87,120],"cellular":[88],"medium,":[89],"no":[91],"other":[92],"dynamic":[93],"element":[94],"than":[95],"memristors,":[98],"hence":[99],"attribute":[101],"all-memristor":[102],"coined":[103],"address":[105],"it":[106],"paper,":[109],"found":[111],"support":[113],"complex":[114],"phenomena.":[115],"The":[116],"destabilization":[117],"solution":[121],"occurs":[122],"second-order":[125],"array":[127],"circuit":[135,179],"parameters":[136],"are":[137],"chosen":[138],"A":[145],"deep":[146],"circuit-":[147],"system-theoretic":[149],"investigation,":[150,157],"including":[151],"linearization":[152],"analysis":[153],"phase":[155],"portrait":[156],"provides":[158],"comprehensive":[160],"picture":[161],"for":[162],"local":[164],"global":[166],"dynamics":[167],"bio-inspired":[170],"revealing":[172],"how":[173],"theory-assisted":[175],"approach":[176],"guide":[178],"design":[180],"inherently":[182],"non-linear":[183],"devices.":[185]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":7}],"updated_date":"2026-03-24T08:02:53.985720","created_date":"2025-10-10T00:00:00"}
