{"id":"https://openalex.org/W3212126961","doi":"https://doi.org/10.1109/tcsi.2021.3123286","title":"A 555 Timer IC Chaotic Circuit: Chaos in a Piecewise Linear System With Stable but No Unstable Equilibria","display_name":"A 555 Timer IC Chaotic Circuit: Chaos in a Piecewise Linear System With Stable but No Unstable Equilibria","publication_year":2021,"publication_date":"2021-11-04","ids":{"openalex":"https://openalex.org/W3212126961","doi":"https://doi.org/10.1109/tcsi.2021.3123286","mag":"3212126961"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2021.3123286","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2021.3123286","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/A5081340107","display_name":"Peera Niranatlumpong","orcid":"https://orcid.org/0000-0002-1125-2460"},"institutions":[{"id":"https://openalex.org/I25399158","display_name":"Mahidol University","ror":"https://ror.org/01znkr924","country_code":"TH","type":"education","lineage":["https://openalex.org/I25399158"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Peera Niranatlumpong","raw_affiliation_strings":["Physics Department, Faculty of Science, Mahidol University, Bangkok, Thailand"],"affiliations":[{"raw_affiliation_string":"Physics Department, Faculty of Science, Mahidol University, Bangkok, Thailand","institution_ids":["https://openalex.org/I25399158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009907592","display_name":"Michael A. Allen","orcid":"https://orcid.org/0000-0003-1495-6970"},"institutions":[{"id":"https://openalex.org/I25399158","display_name":"Mahidol University","ror":"https://ror.org/01znkr924","country_code":"TH","type":"education","lineage":["https://openalex.org/I25399158"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Michael A. Allen","raw_affiliation_strings":["Physics Department, Faculty of Science, Mahidol University, Bangkok, Thailand"],"affiliations":[{"raw_affiliation_string":"Physics Department, Faculty of Science, Mahidol University, Bangkok, Thailand","institution_ids":["https://openalex.org/I25399158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081340107"],"corresponding_institution_ids":["https://openalex.org/I25399158"],"apc_list":null,"apc_paid":null,"fwci":0.9087,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.74536855,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"69","issue":"2","first_page":"798","last_page":"810"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9987000226974487,"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/T10244","display_name":"Chaos control and synchronization","score":0.9987000226974487,"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":0.995199978351593,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.974399983882904,"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/resistor","display_name":"Resistor","score":0.5849670767784119},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5523954033851624},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5451385974884033},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5415239334106445},{"id":"https://openalex.org/keywords/timer","display_name":"Timer","score":0.48016825318336487},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4690314531326294},{"id":"https://openalex.org/keywords/cascade","display_name":"Cascade","score":0.45999181270599365},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.43427878618240356},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4238795042037964},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.41429728269577026},{"id":"https://openalex.org/keywords/capacitor","display_name":"Capacitor","score":0.4128600060939789},{"id":"https://openalex.org/keywords/rl-circuit","display_name":"RL circuit","score":0.4123693108558655},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3882811665534973},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3075578212738037},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.278936505317688},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22013545036315918},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.18987396359443665},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.18827497959136963},{"id":"https://openalex.org/keywords/microcontroller","display_name":"Microcontroller","score":0.1437404453754425}],"concepts":[{"id":"https://openalex.org/C137488568","wikidata":"https://www.wikidata.org/wiki/Q5321","display_name":"Resistor","level":3,"score":0.5849670767784119},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5523954033851624},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5451385974884033},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5415239334106445},{"id":"https://openalex.org/C2776633867","wikidata":"https://www.wikidata.org/wiki/Q186612","display_name":"Timer","level":3,"score":0.48016825318336487},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4690314531326294},{"id":"https://openalex.org/C34146451","wikidata":"https://www.wikidata.org/wiki/Q5048094","display_name":"Cascade","level":2,"score":0.45999181270599365},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.43427878618240356},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4238795042037964},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.41429728269577026},{"id":"https://openalex.org/C52192207","wikidata":"https://www.wikidata.org/wiki/Q5322","display_name":"Capacitor","level":3,"score":0.4128600060939789},{"id":"https://openalex.org/C78457404","wikidata":"https://www.wikidata.org/wiki/Q1836061","display_name":"RL circuit","level":5,"score":0.4123693108558655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3882811665534973},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3075578212738037},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.278936505317688},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22013545036315918},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.18987396359443665},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.18827497959136963},{"id":"https://openalex.org/C173018170","wikidata":"https://www.wikidata.org/wiki/Q165678","display_name":"Microcontroller","level":2,"score":0.1437404453754425},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C29586797","wikidata":"https://www.wikidata.org/wiki/Q5163663","display_name":"Constant power circuit","level":4,"score":0.0},{"id":"https://openalex.org/C64424096","wikidata":"https://www.wikidata.org/wiki/Q750454","display_name":"Power factor","level":3,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2021.3123286","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2021.3123286","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":[{"id":"https://openalex.org/F4320322401","display_name":"Mahidol University","ror":"https://ror.org/01znkr924"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1967332757","https://openalex.org/W1970189657","https://openalex.org/W1971396077","https://openalex.org/W1972634840","https://openalex.org/W1972807647","https://openalex.org/W1990987436","https://openalex.org/W2003768786","https://openalex.org/W2004856923","https://openalex.org/W2011227277","https://openalex.org/W2012578401","https://openalex.org/W2017743925","https://openalex.org/W2020572193","https://openalex.org/W2022294187","https://openalex.org/W2030496841","https://openalex.org/W2031604902","https://openalex.org/W2046383754","https://openalex.org/W2059471761","https://openalex.org/W2060587651","https://openalex.org/W2061372905","https://openalex.org/W2070724789","https://openalex.org/W2080761408","https://openalex.org/W2083823140","https://openalex.org/W2109547066","https://openalex.org/W2110296489","https://openalex.org/W2120058330","https://openalex.org/W2123972824","https://openalex.org/W2141662965","https://openalex.org/W2143976842","https://openalex.org/W2164315701","https://openalex.org/W2182249101","https://openalex.org/W2289853499","https://openalex.org/W2460205926","https://openalex.org/W2585728124","https://openalex.org/W2723497896","https://openalex.org/W2789742277","https://openalex.org/W2960095010","https://openalex.org/W2972978930","https://openalex.org/W3025587973","https://openalex.org/W3036357317","https://openalex.org/W3112904976","https://openalex.org/W3139528947","https://openalex.org/W3154242114","https://openalex.org/W4240452402","https://openalex.org/W4388249796"],"related_works":["https://openalex.org/W2360439717","https://openalex.org/W2765214557","https://openalex.org/W2388292776","https://openalex.org/W2361181213","https://openalex.org/W1031622928","https://openalex.org/W2350005463","https://openalex.org/W2347554032","https://openalex.org/W1459934432","https://openalex.org/W2064165820","https://openalex.org/W2494468374"],"abstract_inverted_index":{"The":[0,38,101,171],"555":[1,24],"timer":[2],"IC":[3,39],"is":[4,79,103,173],"a":[5,14,19,22,42,89,111,116,121],"well-known":[6],"integrated":[7],"circuit":[8,20,65,102,150,172],"having":[9],"been":[10],"widely":[11],"used":[12],"as":[13,41],"pulse":[15],"generator.":[16],"We":[17],"propose":[18],"containing":[21],"single":[23],"IC,":[25],"an":[26,28,169],"LED,":[27],"inductor,":[29],"two":[30,55,99],"capacitors,":[31],"and":[32,115,125],"three":[33,145],"resistors":[34,147],"that":[35,70,156],"exhibits":[36],"chaos.":[37],"serves":[40],"hysteretic":[43,141],"switch":[44],"causing":[45],"the":[46,62,80,95,136,149,152,157,163,166],"system":[47],"to":[48,52,60,118],"be":[49,61,160],"alternately":[50],"attracted":[51],"each":[53],"of":[54,98,135,144,168],"stable":[56,72],"equilibria.":[57,76],"Ours":[58],"appears":[59],"first":[63],"chaotic":[64],"governed":[66],"by":[67,179],"piecewise-linear":[68],"equations":[69],"have":[71],"but":[73],"no":[74],"unstable":[75],"Also":[77],"unique":[78],"sensitive":[81],"dependence":[82],"on":[83],"initial":[84],"conditions":[85],"resulting":[86],"only":[87],"from":[88,94],"square-root":[90],"map.":[91],"This":[92,124],"arises":[93],"grazing":[96],"impact":[97],"voltages.":[100],"also":[104,175],"unusual":[105],"in":[106,131,148],"exhibiting":[107],"periodic":[108],"orbits":[109],"with":[110,133,140,182],"Farey":[112],"tree":[113],"structure":[114],"transition":[117],"chaos":[119],"via":[120,162],"period-adding":[122],"cascade.":[123],"other":[126],"bifurcations":[127,158],"seen":[128],"experimentally":[129],"are":[130],"agreement":[132],"those":[134],"governing":[137],"three-dimensional":[138],"ODEs":[139],"conditions.":[142],"Inclusion":[143],"extra":[146],"lowers":[151],"characteristic":[153],"frequency":[154],"so":[155],"can":[159],"detected":[161],"LED":[164],"without":[165],"need":[167],"oscilloscope.":[170],"therefore":[174],"suitable":[176],"for":[177],"experimentation":[178],"electronics":[180],"hobbyists":[181],"limited":[183],"resources.":[184]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}