{"id":"https://openalex.org/W1995725546","doi":"https://doi.org/10.1109/tcsi.2014.2304655","title":"Designing Hyperchaotic Systems With &lt;newline/&gt;Any Desired Number of Positive Lyapunov &lt;newline/&gt;Exponents via A Simple Model","display_name":"Designing Hyperchaotic Systems With &lt;newline/&gt;Any Desired Number of Positive Lyapunov &lt;newline/&gt;Exponents via A Simple Model","publication_year":2014,"publication_date":"2014-03-04","ids":{"openalex":"https://openalex.org/W1995725546","doi":"https://doi.org/10.1109/tcsi.2014.2304655","mag":"1995725546"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2014.2304655","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2014.2304655","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/A5026612942","display_name":"Chaowen Shen","orcid":null},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chaowen Shen","raw_affiliation_strings":["College of Automation, Guangdong University of Technology, Guangzhou, China","College of automation, Guangdong University of Technology, Guangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]},{"raw_affiliation_string":"College of automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013127565","display_name":"Simin Yu","orcid":"https://orcid.org/0000-0002-1192-6955"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Simin Yu","raw_affiliation_strings":["College of Automation, Guangdong University of Technology, Guangzhou, China","College of automation, Guangdong University of Technology, Guangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]},{"raw_affiliation_string":"College of automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027725400","display_name":"Jinhu L\u00fc","orcid":"https://orcid.org/0000-0003-0275-8387"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinhu Lu","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","Academy of Mathematics and Systems Science, Chinese Academy Of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy Of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024633466","display_name":"Guanrong Chen","orcid":"https://orcid.org/0000-0003-1381-7418"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Guanrong Chen","raw_affiliation_strings":["Department of Electronic Engineering, City University of Hong Kong, Hong Kong","Department of Electronic Engineering; City University of Hong Kong; Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Department of Electronic Engineering; City University of Hong Kong; Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.8109,"has_fulltext":false,"cited_by_count":130,"citation_normalized_percentile":{"value":0.98818217,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"61","issue":"8","first_page":"2380","last_page":"2389"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","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"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9980999827384949,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9955000281333923,"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/dissipative-system","display_name":"Dissipative system","score":0.6971890926361084},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5463848114013672},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.546256422996521},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.5353116989135742},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49883222579956055},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4678640365600586},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4507265090942383},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.4294242262840271},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35684579610824585},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.35576486587524414},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3537423014640808},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34934109449386597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3053523302078247},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16775363683700562},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.14847183227539062},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12460723519325256},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11346882581710815},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.10277414321899414}],"concepts":[{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.6971890926361084},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5463848114013672},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.546256422996521},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5353116989135742},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49883222579956055},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4678640365600586},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4507265090942383},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.4294242262840271},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35684579610824585},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35576486587524414},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3537423014640808},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34934109449386597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3053523302078247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16775363683700562},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.14847183227539062},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12460723519325256},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11346882581710815},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.10277414321899414},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2014.2304655","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2014.2304655","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5099999904632568}],"awards":[{"id":"https://openalex.org/G1050162453","display_name":null,"funder_award_id":"61203148","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2097099975","display_name":null,"funder_award_id":"S2011010001018","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G4537342742","display_name":null,"funder_award_id":"11072254","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5945028132","display_name":"\u57fa\u4e8e\u53cd\u63a7\u5236\u7684\u8fde\u7eed\u65f6\u95f4\u6df7\u6c8c\u7cfb\u7edf\u5efa\u6a21\u65b0\u65b9\u6cd5\u53ca\u5e94\u7528\u7814\u7a76","funder_award_id":"61172023","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6021341360","display_name":null,"funder_award_id":"61025017","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1979244202","https://openalex.org/W1987482599","https://openalex.org/W1998942494","https://openalex.org/W2010970807","https://openalex.org/W2015545173","https://openalex.org/W2017429699","https://openalex.org/W2020427565","https://openalex.org/W2021684685","https://openalex.org/W2031440207","https://openalex.org/W2031668778","https://openalex.org/W2034421105","https://openalex.org/W2036870441","https://openalex.org/W2037979616","https://openalex.org/W2046035016","https://openalex.org/W2066647300","https://openalex.org/W2066910975","https://openalex.org/W2076924412","https://openalex.org/W2079589234","https://openalex.org/W2088247712","https://openalex.org/W2098127225","https://openalex.org/W2107883576","https://openalex.org/W2108504478","https://openalex.org/W2134100806","https://openalex.org/W2135413047","https://openalex.org/W2135827536","https://openalex.org/W2136221998","https://openalex.org/W2317860537","https://openalex.org/W3102494565","https://openalex.org/W4297900861"],"related_works":["https://openalex.org/W2007405763","https://openalex.org/W2371200319","https://openalex.org/W2367609594","https://openalex.org/W3136087161","https://openalex.org/W1486373823","https://openalex.org/W2119578520","https://openalex.org/W2053762185","https://openalex.org/W2913611334","https://openalex.org/W1984283682","https://openalex.org/W1979419366"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3,22,51,73,110,114,213],"new":[4,214],"and":[5,129],"unified":[6],"approach":[7,215],"for":[8,76,151,216],"designing":[9],"desirable":[10,219],"dissipative":[11,77,159,220],"hyperchaotic":[12,78,160,221],"systems.":[13,222],"Based":[14,69],"on":[15,70,119],"the":[16,46,64,89,92,95,104,120,123,130,141,145,186,200,203,209,230,233],"anti-control":[17],"principle":[18],"of":[19,25,91,122,125,132,136,147,193,202,232],"continuous-time":[20],"systems,":[21],"nominal":[23],"system":[24,48,65,161,187,204],"<formula":[26,153,165,174],"formulatype=\"inline\"":[27,154,166,175],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[28,155,167,176],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[29,156],"Notation=\"TeX\">$n":[30,179],"~~(n":[31],"\\geq":[32,180],"5)$</tex></formula>":[33],"independent":[34],"first-order":[35],"linear":[36],"differential":[37],"equations":[38],"are":[39,106,226],"coupled":[40],"through":[41],"all":[42,103],"state":[43,61],"variables,":[44],"making":[45],"controlled":[47],"be":[49],"in":[50,109,184],"closed-loop":[52,96],"cascade-coupling":[53,97],"form,":[54,98],"where":[55],"each":[56],"equation":[57],"contains":[58],"only":[59],"two":[60,224],"variables":[62],"therefore":[63],"is":[66,80,100,117,162,205],"quite":[67],"simple.":[68],"this":[71],"setting,":[72],"simple":[74,143],"model":[75],"systems":[79],"constructed,":[81],"with":[82],"an":[83],"adjustable":[84],"parameter":[85],"which":[86],"can":[87,188],"ensure":[88],"dissipation":[90],"system.":[93],"In":[94],"it":[99],"shown":[101],"that":[102],"eigenvalues":[105],"symmetrically":[107],"distributed":[108],"circumferential":[111],"manner.":[112],"Consequently,":[113],"universal":[115],"law":[116],"derived":[118],"relationship":[121],"number":[124,131,146,192],"positive":[126,133,148,194],"Lyapunov":[127,149,195],"exponents":[128,150,196],"real":[134],"parts":[135],"its":[137],"Jacobian":[138],"eigenvalues.":[139],"For":[140],"above-mentioned":[142],"model,":[144],"any":[152,190],"Notation=\"TeX\">$n$</tex></formula>":[157],"-dimensional":[158],"given":[163,227],"by":[164],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[168,177],"<tex":[169,178],"Notation=\"TeX\">$N=":[170],"{\\rm":[171],"round}((n-1)/2)$</tex></formula>":[172],",":[173],"5$</tex></formula>":[181],".":[182],"Therefore,":[183],"theory,":[185],"generate":[189],"desired":[191],"as":[197,199],"long":[198],"dimension":[201],"sufficiently":[206],"high.":[207],"Thus,":[208],"proposed":[210,234],"method":[211],"provides":[212],"purposefully":[217],"constructing":[218],"Finally,":[223],"examples":[225],"to":[228],"demonstrate":[229],"feasibility":[231],"design":[235],"method.":[236]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
