{"id":"https://openalex.org/W4207006543","doi":"https://doi.org/10.1109/tcsi.2021.3133627","title":"Edge of Chaos Theory Resolves Smale Paradox","display_name":"Edge of Chaos Theory Resolves Smale Paradox","publication_year":2022,"publication_date":"2022-01-21","ids":{"openalex":"https://openalex.org/W4207006543","doi":"https://doi.org/10.1109/tcsi.2021.3133627"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2021.3133627","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2021.3133627","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":6.9064,"has_fulltext":false,"cited_by_count":79,"citation_normalized_percentile":{"value":0.97757444,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"69","issue":"3","first_page":"1252","last_page":"1265"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9998999834060669,"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":0.9998999834060669,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9994000196456909,"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":0.9991999864578247,"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/memristor","display_name":"Memristor","score":0.7773851752281189},{"id":"https://openalex.org/keywords/edge-of-chaos","display_name":"Edge of chaos","score":0.6809212565422058},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5374738574028015},{"id":"https://openalex.org/keywords/multistability","display_name":"Multistability","score":0.4722301959991455},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4663523733615875},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3941948115825653},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38495030999183655},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.34509560465812683},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21336627006530762},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15963032841682434},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11274659633636475}],"concepts":[{"id":"https://openalex.org/C150072547","wikidata":"https://www.wikidata.org/wiki/Q212923","display_name":"Memristor","level":2,"score":0.7773851752281189},{"id":"https://openalex.org/C2780713532","wikidata":"https://www.wikidata.org/wiki/Q93158","display_name":"Edge of chaos","level":2,"score":0.6809212565422058},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5374738574028015},{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.4722301959991455},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4663523733615875},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3941948115825653},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38495030999183655},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.34509560465812683},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21336627006530762},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15963032841682434},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11274659633636475},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2021.3133627","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2021.3133627","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":27,"referenced_works":["https://openalex.org/W29182310","https://openalex.org/W577520130","https://openalex.org/W1606202192","https://openalex.org/W1980661496","https://openalex.org/W1992963104","https://openalex.org/W1993214330","https://openalex.org/W2018341541","https://openalex.org/W2019061854","https://openalex.org/W2030834420","https://openalex.org/W2078594062","https://openalex.org/W2092704633","https://openalex.org/W2095993878","https://openalex.org/W2101091847","https://openalex.org/W2129610161","https://openalex.org/W2153653041","https://openalex.org/W2399958287","https://openalex.org/W2500183209","https://openalex.org/W2891281574","https://openalex.org/W2900178210","https://openalex.org/W2994164165","https://openalex.org/W3099086962","https://openalex.org/W3156265125","https://openalex.org/W3198585701","https://openalex.org/W3217208965","https://openalex.org/W3217786002","https://openalex.org/W4241884932","https://openalex.org/W6645045626"],"related_works":["https://openalex.org/W3035288648","https://openalex.org/W3159427064","https://openalex.org/W4308963954","https://openalex.org/W2383947793","https://openalex.org/W2770598252","https://openalex.org/W4301628837","https://openalex.org/W1973200562","https://openalex.org/W3022993598","https://openalex.org/W3215941631","https://openalex.org/W2893705961"],"abstract_inverted_index":{"No":[0],"isolated":[1],"system":[2],"may":[3,9,72,128,242],"ever":[4],"support":[5],"complexity.":[6],"Emergent":[7],"phenomena":[8,127],"however":[10],"appear":[11],"in":[12,37,74,110,130,162],"an":[13,40,226],"open":[14,152],"system,":[15,153],"if,":[16],"as":[17,100],"established":[18],"by":[19,160],"the":[20,31,84,94,121,149,156,189,220,230,251,255],"Edge":[21,101],"of":[22,26,49,76,93,102,115,138,222,229,254],"Chaos":[23],"theory,":[24],"some":[25],"its":[27,237],"constitutive":[28],"elements":[29],"feature":[30],"capability":[32],"to":[33,55,99,225,249,258],"amplify":[34],"infinitesimal":[35],"fluctuations":[36],"energy,":[38],"provided":[39],"external":[41],"source":[42],"supplies":[43],"them":[44],"with":[45],"a":[46,57,90,106,112,131,167,233,246],"sufficient":[47],"amount":[48],"DC":[50,201],"power,":[51],"which":[52,105,154],"is":[53,87],"known":[54],"be":[56,243],"signature":[58],"for":[59,120,236],"locally-active":[60],"behaviour.":[61],"In":[62],"particular,":[63],"complex":[64],"behaviours,":[65],"including":[66],"static":[67],"and":[68,81,210,239],"dynamic":[69],"pattern":[70],"formation,":[71],"emerge":[73,129],"arrays":[75],"identical":[77,140,175],"diffusively-coupled":[78,141],"cells,":[79,177],"if":[80,83],"only":[82,195],"basic":[85,132],"unit":[86],"poised":[88],"on":[89,180],"particular":[91],"sub-domain":[92],"Local":[95,223],"Activity":[96,224],"regime,":[97],"referred":[98],"Chaos,":[103],"within":[104],"quiet":[107],"state":[108],"hides":[109],"fact":[111],"high":[113],"degree":[114],"excitability.":[116],"Here":[117],"we":[118],"show,":[119],"first":[122],"time,":[123],"that":[124],"these":[125],"counterintuitive":[126],"memristor":[133,231],"cellular":[134,170],"neural":[135],"network,":[136],"consisting":[137],"two":[139,174,200,207,211],"second-order":[142],"cells.":[143],"The":[144],"proposed":[145],"bio-inspired":[146,190],"array":[147,257],"represents":[148],"simplest":[150],"ever-reported":[151],"reproduces":[155],"shocking":[157],"phenomenon,":[158],"reported":[159],"Smale":[161],"1974,":[163],"when,":[164],"while":[165],"studying":[166],"model":[168,228],"from":[169,217],"biology,":[171],"he":[172],"observed":[173],"reaction":[176],"\u201cmathematically":[178],"dead\u201d":[179],"their":[181],"own,":[182],"pulsating":[183],"together":[184],"upon":[185],"diffusive":[186],"coupling.":[187],"Impressively,":[188],"two-cell":[191,256],"reaction-diffusion":[192],"network":[193],"contains":[194],"nine":[196],"circuit":[197],"elements,":[198],"specifically":[199],"voltage":[202],"sources,":[203],"three":[204],"linear":[205,208],"resistors,":[206],"capacitors,":[209],"functional":[212],"niobium":[213],"oxide":[214],"(NbO)":[215],"memristors":[216],"NaMLab.":[218],"Applying":[219],"theory":[221],"accurate":[227],"oscillator,":[232],"comprehensive":[234],"picture":[235],"local":[238],"global":[240],"dynamics":[241],"drawn,":[244],"providing":[245],"systematic":[247],"method":[248],"tune":[250],"design":[252],"parameters":[253],"enable":[259],"diffusion-driven":[260],"instabilities":[261],"therein.":[262]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":24},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-24T08:02:53.985720","created_date":"2025-10-10T00:00:00"}
