{"id":"https://openalex.org/W1981107572","doi":"https://doi.org/10.1142/s0218127405012041","title":"CHAOTIFICATION OF DISCRETE-TIME DYNAMICAL SYSTEMS: AN EXTENSION OF THE CHEN\u2013LAI ALGORITHM","display_name":"CHAOTIFICATION OF DISCRETE-TIME DYNAMICAL SYSTEMS: AN EXTENSION OF THE CHEN\u2013LAI ALGORITHM","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1981107572","doi":"https://doi.org/10.1142/s0218127405012041","mag":"1981107572"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405012041","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405012041","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5059257496","display_name":"Dejian Lai","orcid":"https://orcid.org/0000-0003-1927-8021"},"institutions":[{"id":"https://openalex.org/I59649739","display_name":"Jiangxi University of Finance and Economics","ror":"https://ror.org/03efmyj29","country_code":"CN","type":"education","lineage":["https://openalex.org/I59649739"]},{"id":"https://openalex.org/I919571938","display_name":"The University of Texas Health Science Center at Houston","ror":"https://ror.org/03gds6c39","country_code":"US","type":"education","lineage":["https://openalex.org/I919571938"]}],"countries":["CN","US"],"is_corresponding":true,"raw_author_name":"DEJIAN LAI","raw_affiliation_strings":["Division of Biostatistics, School of Public Health, University of Texas, Houston, TX 77030, USA","Faculty of Statistics, JiangXi University of Finance and Economics Nanchang, P. R. China"],"affiliations":[{"raw_affiliation_string":"Division of Biostatistics, School of Public Health, University of Texas, Houston, TX 77030, USA","institution_ids":["https://openalex.org/I919571938"]},{"raw_affiliation_string":"Faculty of Statistics, JiangXi University of Finance and Economics Nanchang, P. R. China","institution_ids":["https://openalex.org/I59649739"]}]},{"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, Kowloon, Hong Kong, P. R. China","Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong, P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong, P. R. China","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong, P.R. China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5059257496"],"corresponding_institution_ids":["https://openalex.org/I59649739","https://openalex.org/I919571938"],"apc_list":null,"apc_paid":null,"fwci":1.24955429,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.76778877,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"01","first_page":"109","last_page":"117"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9983000159263611,"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/T12158","display_name":"Guidance and Control Systems","score":0.982200026512146,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.8124581575393677},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.7257028818130493},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.722037672996521},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7015746831893921},{"id":"https://openalex.org/keywords/chen","display_name":"Chen","score":0.6578257083892822},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.6221427917480469},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6138057112693787},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5687910318374634},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5226778388023376},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4692996144294739},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4674082100391388},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4571322202682495},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35280951857566833},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3359018564224243},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2770722508430481},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25096118450164795},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.19456949830055237},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12169870734214783},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07114848494529724},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07032826542854309}],"concepts":[{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.8124581575393677},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.7257028818130493},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.722037672996521},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7015746831893921},{"id":"https://openalex.org/C2776085556","wikidata":"https://www.wikidata.org/wiki/Q183361","display_name":"Chen","level":2,"score":0.6578257083892822},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.6221427917480469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6138057112693787},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5687910318374634},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5226778388023376},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4692996144294739},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4674082100391388},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4571322202682495},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35280951857566833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3359018564224243},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2770722508430481},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25096118450164795},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.19456949830055237},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12169870734214783},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07114848494529724},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07032826542854309},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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:10.1142/s0218127405012041","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405012041","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1985039283","https://openalex.org/W2018738409","https://openalex.org/W2024026135","https://openalex.org/W2040298053","https://openalex.org/W2055696663","https://openalex.org/W2076906073","https://openalex.org/W2104508228","https://openalex.org/W2139153229","https://openalex.org/W2179264759","https://openalex.org/W2321551058","https://openalex.org/W2346714215","https://openalex.org/W2403035479","https://openalex.org/W2574026466","https://openalex.org/W4206744643","https://openalex.org/W4248796009"],"related_works":["https://openalex.org/W2230606337","https://openalex.org/W4250831671","https://openalex.org/W2089869689","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2504224383","https://openalex.org/W2377513064","https://openalex.org/W2016990342","https://openalex.org/W2952544653"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"propose":[4],"and":[5],"study":[6],"an":[7],"extension":[8],"of":[9,15,40],"the":[10,37,41],"Chen\u2013Lai":[11],"algorithm":[12],"for":[13,46],"chaotification":[14],"discrete-time":[16],"dynamical":[17,50],"systems.":[18],"The":[19],"proposed":[20],"method":[21,31],"is":[22],"a":[23,54],"simple":[24],"but":[25,58],"mathematically":[26],"rigorous":[27],"feedback":[28],"control":[29],"design":[30],"that":[32,52],"can":[33],"gradually":[34],"make":[35],"all":[36],"Lyapunov":[38],"exponents":[39],"controlled":[42],"system":[43,51],"strictly":[44],"positive":[45],"any":[47],"given":[48],"n-dimensional":[49],"has":[53],"uniformly":[55],"bounded":[56],"Jacobian":[57],"otherwise":[59],"could":[60],"be":[61],"originally":[62],"nonchaotic":[63],"or":[64],"even":[65],"asymptotically":[66],"stable.":[67]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}