{"id":"https://openalex.org/W2153903365","doi":"https://doi.org/10.1142/s021812740601629x","title":"CHAOTIFICATION OF DISCRETE DYNAMICAL SYSTEMS IN BANACH SPACES","display_name":"CHAOTIFICATION OF DISCRETE DYNAMICAL SYSTEMS IN BANACH SPACES","publication_year":2006,"publication_date":"2006-09-01","ids":{"openalex":"https://openalex.org/W2153903365","doi":"https://doi.org/10.1142/s021812740601629x","mag":"2153903365"},"language":"en","primary_location":{"id":"doi:10.1142/s021812740601629x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740601629x","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/A5101948112","display_name":"Yuming Shi","orcid":"https://orcid.org/0000-0002-8609-2377"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]},{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CA","CN"],"is_corresponding":true,"raw_author_name":"YUMING SHI","raw_affiliation_strings":["Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada","Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada","institution_ids":["https://openalex.org/I125749732"]},{"raw_affiliation_string":"Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100652002","display_name":"Pei Yu","orcid":"https://orcid.org/0000-0002-8848-0584"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"PEI YU","raw_affiliation_strings":["Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"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, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, City University of Hong Kong, P. R. China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101948112"],"corresponding_institution_ids":["https://openalex.org/I125749732","https://openalex.org/I154099455"],"apc_list":null,"apc_paid":null,"fwci":3.1617,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.9265588,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"09","first_page":"2615","last_page":"2636"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9957000017166138,"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/mathematics","display_name":"Mathematics","score":0.7815006971359253},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7733142971992493},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6644737720489502},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5477345585823059},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5228350758552551},{"id":"https://openalex.org/keywords/sense","display_name":"Sense (electronics)","score":0.4475480020046234},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4453681707382202},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.4336036443710327},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4328201413154602},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.42063236236572266},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3493618965148926},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.33110812306404114},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15658199787139893}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7815006971359253},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7733142971992493},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6644737720489502},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5477345585823059},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5228350758552551},{"id":"https://openalex.org/C143141573","wikidata":"https://www.wikidata.org/wiki/Q7450971","display_name":"Sense (electronics)","level":2,"score":0.4475480020046234},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4453681707382202},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.4336036443710327},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4328201413154602},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.42063236236572266},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3493618965148926},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33110812306404114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15658199787139893},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s021812740601629x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740601629x","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.259.8785","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.259.8785","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://pyu1.apmaths.uwo.ca/%7Epyu/pub/preprints/SYC_IJBC2006.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W37225765","https://openalex.org/W596968612","https://openalex.org/W659295881","https://openalex.org/W1496745782","https://openalex.org/W1543724297","https://openalex.org/W1598317411","https://openalex.org/W1970135831","https://openalex.org/W1979684610","https://openalex.org/W1984136276","https://openalex.org/W1985039283","https://openalex.org/W1994429651","https://openalex.org/W1998538686","https://openalex.org/W2002681938","https://openalex.org/W2008995486","https://openalex.org/W2017751505","https://openalex.org/W2024026135","https://openalex.org/W2024306217","https://openalex.org/W2028985073","https://openalex.org/W2040112596","https://openalex.org/W2042083138","https://openalex.org/W2043865975","https://openalex.org/W2043992273","https://openalex.org/W2055660413","https://openalex.org/W2058791052","https://openalex.org/W2059340344","https://openalex.org/W2067904577","https://openalex.org/W2076906073","https://openalex.org/W2120706888","https://openalex.org/W2139153229","https://openalex.org/W2154619247","https://openalex.org/W2166393890","https://openalex.org/W2488944911","https://openalex.org/W2577900305","https://openalex.org/W3038830718","https://openalex.org/W3138265894","https://openalex.org/W4206744643","https://openalex.org/W4235485079","https://openalex.org/W4235783284","https://openalex.org/W4239883234","https://openalex.org/W4248796009","https://openalex.org/W4252563066","https://openalex.org/W4252910012","https://openalex.org/W4294967943","https://openalex.org/W4302770682"],"related_works":["https://openalex.org/W4250831671","https://openalex.org/W2230606337","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2330535098","https://openalex.org/W2377513064","https://openalex.org/W2952544653"],"abstract_inverted_index":{"This":[0,27],"paper":[1],"is":[2,24,80,134,146,171,204],"concerned":[3],"with":[4,127,206],"chaotification":[5],"of":[6,19,58,88,95,152,160,192,199],"discrete":[7],"dynamical":[8],"systems":[9,49],"in":[10,21,39,55,70,85,92,114,129,149,157,187],"Banach":[11,22,44,140],"spaces":[12,23],"via":[13,124],"feedback":[14,112,125],"control":[15,113,126],"techniques.":[16],"A":[17],"criterion":[18,28],"chaos":[20],"first":[25],"established.":[26],"extends":[29],"and":[30,41,61,78,142,163],"improves":[31],"the":[32,47,56,86,93,120,143,150,158,176,180,193],"Marotto":[33],"theorem.":[34],"Discussions":[35],"are":[36,50],"carried":[37],"out":[38],"general":[40],"some":[42,188,207],"special":[43],"spaces.":[45],"All":[46],"controlled":[48,67,144],"proved":[51],"to":[52,103,136,179,196],"be":[53,101,104],"chaotic":[54,82,105,148],"sense":[57,87,94,151,159],"both":[59,161],"Devaney":[60,153],"Li\u2013Yorke.":[62],"As":[63],"a":[64,66,71,115,130,137,184,197],"consequence,":[65],"system":[68,99,145,182],"described":[69],"finite-dimensional":[72,131],"real":[73,132],"space":[74,133],"studied":[75],"by":[76,106],"Wang":[77],"Chen":[79],"shown":[81,147],"not":[83,172],"only":[84],"Li\u2013Yorke":[89,162],"but":[90],"also":[91],"Devaney.":[96],"The":[97],"original":[98,181],"can":[100],"driven":[102],"using":[107],"an":[108],"arbitrarily":[109],"small-amplitude":[110],"state":[111],"certain":[116,138],"space.":[117],"In":[118],"addition,":[119],"Chen\u2013Lai":[121],"anti-control":[122],"algorithm":[123],"mod-operation":[128],"extended":[135],"infinite-dimensional":[139],"space,":[141],"as":[154,156],"well":[155],"Wiggins.":[164],"Differing":[165],"from":[166],"many":[167],"existing":[168],"results,":[169],"it":[170],"here":[173],"required":[174],"that":[175],"map":[177],"corresponding":[178],"has":[183],"fixed":[185],"point":[186],"cases.":[189],"An":[190],"application":[191],"theoretical":[194],"results":[195],"class":[198],"first-order":[200],"partial":[201],"difference":[202],"equations":[203],"given":[205],"numerical":[208],"simulations.":[209]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}