{"id":"https://openalex.org/W2040112596","doi":"https://doi.org/10.1142/s0218127405012351","title":"CHAOTIFICATION OF DISCRETE DYNAMICAL SYSTEMS GOVERNED BY CONTINUOUS MAPS","display_name":"CHAOTIFICATION OF DISCRETE DYNAMICAL SYSTEMS GOVERNED BY CONTINUOUS MAPS","publication_year":2005,"publication_date":"2005-02-01","ids":{"openalex":"https://openalex.org/W2040112596","doi":"https://doi.org/10.1142/s0218127405012351","mag":"2040112596"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405012351","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405012351","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/A5101948113","display_name":"Yuming Shi","orcid":null},"institutions":[{"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":["CN"],"is_corresponding":true,"raw_author_name":"YUMING SHI","raw_affiliation_strings":["Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China","institution_ids":["https://openalex.org/I154099455"]}]},{"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":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101948113"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"apc_list":null,"apc_paid":null,"fwci":3.2312,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.92569972,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"15","issue":"02","first_page":"547","last_page":"555"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9944999814033508,"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/T10244","display_name":"Chaos control and synchronization","score":0.9923999905586243,"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/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.7909973859786987},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6763744354248047},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.5685330033302307},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5393578410148621},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5102438926696777},{"id":"https://openalex.org/keywords/feedback-control","display_name":"Feedback control","score":0.4661696255207062},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4374057352542877},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3921999931335449},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3900294899940491},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.35733097791671753},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3380035161972046},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2583163380622864},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12204325199127197},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06448444724082947}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.7909973859786987},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6763744354248047},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.5685330033302307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5393578410148621},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5102438926696777},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.4661696255207062},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4374057352542877},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3921999931335449},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3900294899940491},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.35733097791671753},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3380035161972046},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2583163380622864},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12204325199127197},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06448444724082947},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","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/s0218127405012351","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405012351","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":28,"referenced_works":["https://openalex.org/W596968612","https://openalex.org/W1496745782","https://openalex.org/W1507925093","https://openalex.org/W1589876408","https://openalex.org/W1598317411","https://openalex.org/W1970135831","https://openalex.org/W1985039283","https://openalex.org/W1998538686","https://openalex.org/W2002681938","https://openalex.org/W2024026135","https://openalex.org/W2024306217","https://openalex.org/W2028985073","https://openalex.org/W2042083138","https://openalex.org/W2043992273","https://openalex.org/W2055660413","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/W2574026466","https://openalex.org/W4206744643","https://openalex.org/W4235783284","https://openalex.org/W4239883234","https://openalex.org/W4248796009","https://openalex.org/W4252563066","https://openalex.org/W4252910012"],"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":[0,84],"paper":[1],"is":[2,86],"concerned":[3],"with":[4],"chaotification":[5,19,28],"of":[6,50,82],"discrete":[7,23,33],"dynamical":[8,24,34],"systems":[9,25,35,41,60],"in":[10,47,79,90],"finite-dimensional":[11],"real":[12],"spaces,":[13],"via":[14],"feedback":[15],"control":[16],"techniques.":[17],"A":[18],"theorem":[20,29],"for":[21,30],"one-dimensional":[22],"and":[26,61],"a":[27],"general":[31],"higher-dimensional":[32],"are":[36,42,64],"established,":[37],"respectively.":[38],"The":[39],"controlled":[40],"proved":[43],"to":[44,57,67],"be":[45],"chaotic":[46],"the":[48,54,58,80,91],"sense":[49],"Devaney.":[51],"In":[52],"particular,":[53],"maps":[55],"corresponding":[56],"original":[59],"designed":[62],"controllers":[63],"only":[65],"required":[66],"satisfy":[68],"some":[69],"mild":[70],"assumptions":[71],"on":[72],"two":[73],"very":[74],"small":[75],"disjoint":[76],"closed":[77],"subsets":[78],"domains":[81],"interest.":[83],"condition":[85],"weaker":[87],"than":[88],"those":[89],"existing":[92],"relevant":[93],"literature.":[94]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}