{"id":"https://openalex.org/W2203934738","doi":"https://doi.org/10.3390/e17127882","title":"Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System","display_name":"Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System","publication_year":2015,"publication_date":"2015-12-18","ids":{"openalex":"https://openalex.org/W2203934738","doi":"https://doi.org/10.3390/e17127882","mag":"2203934738"},"language":"en","primary_location":{"id":"doi:10.3390/e17127882","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17127882","pdf_url":"https://www.mdpi.com/1099-4300/17/12/7882/pdf?version=1450444072","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/17/12/7882/pdf?version=1450444072","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075708894","display_name":"Shaobo He","orcid":"https://orcid.org/0000-0001-5190-4841"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shaobo He","raw_affiliation_strings":["School of Physics and Electronics, Central South University Changsha, Changsha 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Electronics, Central South University Changsha, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018654135","display_name":"Kehui Sun","orcid":"https://orcid.org/0000-0002-9292-0263"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]},{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Kehui Sun","raw_affiliation_strings":["School of Physics Science and Technology, Xinjiang University, Urumqi 830046, China","School of Physics and Electronics, Central South University Changsha, Changsha 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics Science and Technology, Xinjiang University, Urumqi 830046, China","institution_ids":["https://openalex.org/I96908189"]},{"raw_affiliation_string":"School of Physics and Electronics, Central South University Changsha, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034892782","display_name":"Huihai Wang","orcid":"https://orcid.org/0000-0002-8660-2795"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huihai Wang","raw_affiliation_strings":["School of Physics and Electronics, Central South University Changsha, Changsha 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Electronics, Central South University Changsha, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018654135"],"corresponding_institution_ids":["https://openalex.org/I139660479","https://openalex.org/I96908189"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":8.5826,"has_fulltext":false,"cited_by_count":211,"citation_normalized_percentile":{"value":0.98147536,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"17","issue":"12","first_page":"8299","last_page":"8311"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9995999932289124,"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":0.9995999932289124,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9731000065803528,"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9625999927520752,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7742273211479187},{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.748323380947113},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.6179751753807068},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.598971426486969},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5093704462051392},{"id":"https://openalex.org/keywords/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.504804253578186},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.47477245330810547},{"id":"https://openalex.org/keywords/nist","display_name":"NIST","score":0.46866095066070557},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4656881093978882},{"id":"https://openalex.org/keywords/logistic-map","display_name":"Logistic map","score":0.45888927578926086},{"id":"https://openalex.org/keywords/adomian-decomposition-method","display_name":"Adomian decomposition method","score":0.45073288679122925},{"id":"https://openalex.org/keywords/h\u00e9non-map","display_name":"H\u00e9non map","score":0.43594467639923096},{"id":"https://openalex.org/keywords/chaotic-systems","display_name":"Chaotic systems","score":0.43566352128982544},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4055103659629822},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39857423305511475},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3847757875919342},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3378910720348358},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.321394681930542},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19864118099212646},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.16077017784118652},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1504889726638794},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1105508804321289},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08510857820510864}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7742273211479187},{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.748323380947113},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.6179751753807068},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.598971426486969},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5093704462051392},{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.504804253578186},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.47477245330810547},{"id":"https://openalex.org/C111219384","wikidata":"https://www.wikidata.org/wiki/Q6954384","display_name":"NIST","level":2,"score":0.46866095066070557},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4656881093978882},{"id":"https://openalex.org/C205330730","wikidata":"https://www.wikidata.org/wiki/Q587182","display_name":"Logistic map","level":3,"score":0.45888927578926086},{"id":"https://openalex.org/C120317633","wikidata":"https://www.wikidata.org/wiki/Q3042796","display_name":"Adomian decomposition method","level":3,"score":0.45073288679122925},{"id":"https://openalex.org/C2781402108","wikidata":"https://www.wikidata.org/wiki/Q1642961","display_name":"H\u00e9non map","level":3,"score":0.43594467639923096},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.43566352128982544},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4055103659629822},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39857423305511475},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3847757875919342},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3378910720348358},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.321394681930542},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19864118099212646},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.16077017784118652},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1504889726638794},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1105508804321289},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08510857820510864},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"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/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e17127882","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17127882","pdf_url":"https://www.mdpi.com/1099-4300/17/12/7882/pdf?version=1450444072","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b76aa3fb7a4149759cdc36bec0245149","is_oa":true,"landing_page_url":"https://doaj.org/article/b76aa3fb7a4149759cdc36bec0245149","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 17, Iss 12, Pp 8299-8311 (2015)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/17/12/7882/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e17127882","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 17; Issue 12; Pages: 8299-8311","raw_type":"Text"},{"id":"pmh:oai:mdpi.com:/1099-4300/17/12/8299/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e17127882","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e17127882","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17127882","pdf_url":"https://www.mdpi.com/1099-4300/17/12/7882/pdf?version=1450444072","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G400819569","display_name":"\u5f3a\u5316\u6df7\u6c8c\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u7279\u6027\u5206\u6790\u4e0e\u7535\u8def\u5b9e\u73b0\u7814\u7a76","funder_award_id":"61161006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5988883953","display_name":null,"funder_award_id":"2014zzts010","funder_id":"https://openalex.org/F4320335880","funder_display_name":"Fundamental Research Funds for Central Universities of the Central South University"},{"id":"https://openalex.org/G7578344","display_name":null,"funder_award_id":"61073187","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/F4320335880","display_name":"Fundamental Research Funds for Central Universities of the Central South University","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W996007806","https://openalex.org/W1965013603","https://openalex.org/W1970940224","https://openalex.org/W1972460455","https://openalex.org/W1975085179","https://openalex.org/W1979449500","https://openalex.org/W1993834776","https://openalex.org/W2006803905","https://openalex.org/W2010835136","https://openalex.org/W2011261693","https://openalex.org/W2014683958","https://openalex.org/W2026103914","https://openalex.org/W2026218703","https://openalex.org/W2030308954","https://openalex.org/W2043347187","https://openalex.org/W2045882715","https://openalex.org/W2046826796","https://openalex.org/W2063439106","https://openalex.org/W2075362850","https://openalex.org/W2082708622","https://openalex.org/W2087217021","https://openalex.org/W2094602679","https://openalex.org/W2095360730","https://openalex.org/W2122474557","https://openalex.org/W2135879504","https://openalex.org/W2152254020","https://openalex.org/W2155572235","https://openalex.org/W2302073895","https://openalex.org/W2587504689","https://openalex.org/W3019955323"],"related_works":["https://openalex.org/W2032632404","https://openalex.org/W1969643210","https://openalex.org/W2010714820","https://openalex.org/W2362177665","https://openalex.org/W1975417053","https://openalex.org/W2392476553","https://openalex.org/W2140640830","https://openalex.org/W1976056526","https://openalex.org/W1600158002","https://openalex.org/W4368370350"],"abstract_inverted_index":{"The":[0,104],"fractional-order":[1,101,105],"hyperchaotic":[2],"Lorenz":[3],"system":[4,24,36,53,77,106],"is":[5,78,107,119],"solved":[6],"as":[7],"a":[8,93,115],"discrete":[9,31],"map":[10],"by":[11,41,64,109],"applying":[12],"the":[13,76,123,128],"Adomian":[14],"decomposition":[15],"method":[16],"(ADM).":[17],"Lyapunov":[18],"Characteristic":[19],"Exponents":[20],"(LCEs)":[21],"of":[22,34,100],"this":[23,29,35,52,70],"are":[25,39],"calculated":[26],"according":[27],"to":[28],"deduced":[30],"map.":[32],"Complexity":[33],"versus":[37],"parameters":[38],"analyzed":[40],"LCEs,":[42],"bifurcation":[43],"diagrams,":[44],"phase":[45],"portraits,":[46],"complexity":[47,90],"algorithms.":[48],"Results":[49],"show":[50],"that":[51,75],"has":[54],"rich":[55],"dynamical":[56],"behaviors.":[57],"Chaos":[58],"and":[59,87,114],"hyperchaos":[60],"can":[61],"be":[62],"generated":[63],"decreasing":[65],"fractional":[66],"order":[67],"q":[68,82],"in":[69],"system.":[71],"It":[72],"also":[73],"shows":[74],"more":[79],"complex":[80],"when":[81],"takes":[83],"smaller":[84],"values.":[85],"SE":[86],"C":[88],"0":[89],"algorithms":[91],"provide":[92],"parameter":[94],"choice":[95],"criteria":[96],"for":[97],"practice":[98],"applications":[99],"chaotic":[102],"systems.":[103],"implemented":[108,124],"digital":[110],"signal":[111],"processor":[112],"(DSP),":[113],"pseudo-random":[116],"bit":[117],"generator":[118],"designed":[120],"based":[121],"on":[122],"system,":[125],"which":[126],"passes":[127],"NIST":[129],"test":[130],"successfully.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":23},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":32},{"year":2019,"cited_by_count":40},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
