{"id":"https://openalex.org/W2095971001","doi":"https://doi.org/10.1109/iscas.2009.5118395","title":"Bifurcation and chaos in the fractional Chua and Chen systems with very low order","display_name":"Bifurcation and chaos in the fractional Chua and Chen systems with very low order","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2095971001","doi":"https://doi.org/10.1109/iscas.2009.5118395","mag":"2095971001"},"language":"en","primary_location":{"id":"doi:10.1109/iscas.2009.5118395","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscas.2009.5118395","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Circuits and Systems","raw_type":"proceedings-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/A5073255599","display_name":"Donato Cafagna","orcid":"https://orcid.org/0000-0002-3804-8021"},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Donato Cafagna","raw_affiliation_strings":["Dipartimento Ingegneria Innovazione, Universit\u00e0 del Salento, Lecce, Italy","Dipartimento Ingegneria Innovazione, Universit\u00e0 del Salento, Lecce - ITALY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento Ingegneria Innovazione, Universit\u00e0 del Salento, Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]},{"raw_affiliation_string":"Dipartimento Ingegneria Innovazione, Universit\u00e0 del Salento, Lecce - ITALY","institution_ids":["https://openalex.org/I142910587"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055199720","display_name":"Giuseppe Grassi","orcid":"https://orcid.org/0000-0002-8876-3760"},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giuseppe Grassi","raw_affiliation_strings":["Dipartimento Ingegneria Innovazione, Universit\u00e0 del Salento, Lecce, Italy","Dipartimento Ingegneria Innovazione, Universit\u00e0 del Salento, Lecce - ITALY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento Ingegneria Innovazione, Universit\u00e0 del Salento, Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]},{"raw_affiliation_string":"Dipartimento Ingegneria Innovazione, Universit\u00e0 del Salento, Lecce - ITALY","institution_ids":["https://openalex.org/I142910587"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I142910587"],"apc_list":null,"apc_paid":null,"fwci":0.2423,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.58179041,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"29","issue":null,"first_page":"2846","last_page":"2849"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9993000030517578,"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":0.9993000030517578,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9990000128746033,"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/chen","display_name":"Chen","score":0.8413971066474915},{"id":"https://openalex.org/keywords/chuas-circuit","display_name":"Chua's circuit","score":0.5975250601768494},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5681378245353699},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5675469040870667},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5585073828697205},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.54334956407547},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.47419506311416626},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4575026333332062},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.41537606716156006},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34208714962005615},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.33188796043395996},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3232104778289795},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27782243490219116},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.2108606994152069},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15924537181854248},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08065727353096008}],"concepts":[{"id":"https://openalex.org/C2776085556","wikidata":"https://www.wikidata.org/wiki/Q183361","display_name":"Chen","level":2,"score":0.8413971066474915},{"id":"https://openalex.org/C2781300247","wikidata":"https://www.wikidata.org/wiki/Q258022","display_name":"Chua's circuit","level":3,"score":0.5975250601768494},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5681378245353699},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5675469040870667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5585073828697205},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.54334956407547},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.47419506311416626},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4575026333332062},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.41537606716156006},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34208714962005615},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.33188796043395996},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3232104778289795},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27782243490219116},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.2108606994152069},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15924537181854248},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08065727353096008},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iscas.2009.5118395","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscas.2009.5118395","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Circuits and Systems","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W55790716","https://openalex.org/W1489022300","https://openalex.org/W1509146820","https://openalex.org/W1560556759","https://openalex.org/W1884789197","https://openalex.org/W2023565590","https://openalex.org/W2027955822","https://openalex.org/W2040722980","https://openalex.org/W2046035016","https://openalex.org/W2069436097","https://openalex.org/W2091877690","https://openalex.org/W2128470802","https://openalex.org/W2133242986","https://openalex.org/W2135879504","https://openalex.org/W2151223939","https://openalex.org/W2154953502","https://openalex.org/W2155572235","https://openalex.org/W2303324995","https://openalex.org/W4247371619","https://openalex.org/W4253062931","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2370310922","https://openalex.org/W2386975637","https://openalex.org/W2891436901","https://openalex.org/W2388837937","https://openalex.org/W2087355708","https://openalex.org/W2385339070","https://openalex.org/W4291238811","https://openalex.org/W2391317366","https://openalex.org/W2349255442","https://openalex.org/W1536339536"],"abstract_inverted_index":{"The":[0,22],"aim":[1],"of":[2,34,49,126,141,146],"this":[3],"work":[4],"is":[5,24,120],"to":[6,39,122,132],"analyze":[7],"the":[8,12,32,35,50,56,66,79,96,108,115,124,135],"chaotic":[9],"behaviors":[10],"in":[11,42,65,83,95,112,134],"fractional-order":[13],"Chua":[14,68],"and":[15,129],"Chen":[16,98,116,137],"systems":[17],"via":[18],"a":[19,27,142],"time-domain":[20,54,144],"approach.":[21],"objective":[23],"achieved":[25],"using":[26],"decomposition":[28],"method,":[29],"which":[30,77,106],"allows":[31],"solution":[33],"fractional":[36,67,97,136],"differential":[37],"equations":[38],"be":[40],"written":[41],"closed":[43],"form.":[44],"Specifically,":[45],"by":[46,53,139],"taking":[47],"advantage":[48],"capabilities":[51],"given":[52],"analysis,":[55],"paper":[57],"illustrates":[58],"three":[59],"remarkable":[60],"findings:":[61],"i)":[62],"chaos":[63,93,133],"exists":[64,94],"system":[69,88,99],"with":[70,100],"very":[71],"low":[72,103],"order,":[73],"that":[74],"is,":[75],"0.03,":[76],"represents":[78,107],"lowest":[80],"order":[81,101],"reported":[82,111],"literature":[84,113],"for":[85,114],"any":[86],"dynamical":[87],"studied":[89],"so":[90],"far;":[91],"ii)":[92],"as":[102,104],"0.24,":[105],"smallest":[109],"value":[110],"system;":[117],"iii)":[118],"it":[119],"feasible":[121],"show":[123],"occurrence":[125],"pitchfork":[127],"bifurcations":[128],"period-doubling":[130],"routes":[131],"system,":[138],"virtue":[140],"systematic":[143],"analysis":[145],"its":[147],"dynamics.":[148]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}