{"id":"https://openalex.org/W3161426381","doi":"https://doi.org/10.1109/access.2021.3081024","title":"Complexity Analysis of Three-Dimensional Fractional-Order Chaotic System Based on Entropy Theory","display_name":"Complexity Analysis of Three-Dimensional Fractional-Order Chaotic System Based on Entropy Theory","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3161426381","doi":"https://doi.org/10.1109/access.2021.3081024","mag":"3161426381"},"language":"en","primary_location":{"id":"doi:10.1109/access.2021.3081024","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3081024","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09432844.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09432844.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100337868","display_name":"Guohui Li","orcid":"https://orcid.org/0000-0001-8175-4311"},"institutions":[{"id":"https://openalex.org/I4210136859","display_name":"Xi\u2019an University of Posts and Telecommunications","ror":"https://ror.org/04jn0td46","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210136859"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guohui Li","raw_affiliation_strings":["School of Electronic Engineering, Xi’an University of Posts & Telecommunications, Xi’an, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Engineering, Xi’an University of Posts & Telecommunications, Xi’an, China","institution_ids":["https://openalex.org/I4210136859"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046765840","display_name":"Xiangyu Zhang","orcid":"https://orcid.org/0000-0003-4551-0840"},"institutions":[{"id":"https://openalex.org/I4210136859","display_name":"Xi\u2019an University of Posts and Telecommunications","ror":"https://ror.org/04jn0td46","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210136859"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangyu Zhang","raw_affiliation_strings":["School of Electronic Engineering, Xi’an University of Posts & Telecommunications, Xi’an, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Engineering, Xi’an University of Posts & Telecommunications, Xi’an, China","institution_ids":["https://openalex.org/I4210136859"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062896696","display_name":"Hong Yang","orcid":"https://orcid.org/0000-0002-7028-5879"},"institutions":[{"id":"https://openalex.org/I4210136859","display_name":"Xi\u2019an University of Posts and Telecommunications","ror":"https://ror.org/04jn0td46","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210136859"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hong Yang","raw_affiliation_strings":["School of Electronic Engineering, Xi’an University of Posts & Telecommunications, Xi’an, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Engineering, Xi’an University of Posts & Telecommunications, Xi’an, China","institution_ids":["https://openalex.org/I4210136859"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100337868"],"corresponding_institution_ids":["https://openalex.org/I4210136859"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.5251,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.63863451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"9","issue":null,"first_page":"73012","last_page":"73028"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9948999881744385,"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":0.9948999881744385,"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/T10320","display_name":"Neural Networks and Applications","score":0.9632999897003174,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9373999834060669,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6734511256217957},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5781590938568115},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.5325300693511963},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5005483627319336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4764176607131958},{"id":"https://openalex.org/keywords/approximate-entropy","display_name":"Approximate entropy","score":0.4671114683151245},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4607250988483429},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46034908294677734},{"id":"https://openalex.org/keywords/sample-entropy","display_name":"Sample entropy","score":0.417094349861145},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3482677638530731},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32204669713974},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.24880394339561462},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1474081575870514},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11242318153381348}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6734511256217957},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5781590938568115},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.5325300693511963},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5005483627319336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4764176607131958},{"id":"https://openalex.org/C86859247","wikidata":"https://www.wikidata.org/wiki/Q4781760","display_name":"Approximate entropy","level":3,"score":0.4671114683151245},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4607250988483429},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46034908294677734},{"id":"https://openalex.org/C66696666","wikidata":"https://www.wikidata.org/wiki/Q17105612","display_name":"Sample entropy","level":3,"score":0.417094349861145},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3482677638530731},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32204669713974},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.24880394339561462},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1474081575870514},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11242318153381348},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2021.3081024","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3081024","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09432844.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ee4c3bd1fd5b42daaf91662142d583a6","is_oa":true,"landing_page_url":"https://doaj.org/article/ee4c3bd1fd5b42daaf91662142d583a6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 9, Pp 73012-73028 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2021.3081024","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3081024","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09432844.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G37568934","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8685861336","display_name":null,"funder_award_id":"51709228","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3161426381.pdf","grobid_xml":"https://content.openalex.org/works/W3161426381.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W1972634840","https://openalex.org/W1984889099","https://openalex.org/W1985832255","https://openalex.org/W2022776892","https://openalex.org/W2025178372","https://openalex.org/W2432419794","https://openalex.org/W2566381922","https://openalex.org/W2587504689","https://openalex.org/W2754238780","https://openalex.org/W2765128141","https://openalex.org/W2791130675","https://openalex.org/W2888781404","https://openalex.org/W2890896706","https://openalex.org/W2896012846","https://openalex.org/W2898913419","https://openalex.org/W2903984117","https://openalex.org/W2913454977","https://openalex.org/W2946548641","https://openalex.org/W2948309443","https://openalex.org/W2949917339","https://openalex.org/W2951138942","https://openalex.org/W2968309144","https://openalex.org/W2971941035","https://openalex.org/W2974377656","https://openalex.org/W2976265833","https://openalex.org/W2982740292","https://openalex.org/W2985259313","https://openalex.org/W2990425192","https://openalex.org/W3005505817","https://openalex.org/W3006142668","https://openalex.org/W3012334039","https://openalex.org/W3013342027","https://openalex.org/W3014639127","https://openalex.org/W3015145613","https://openalex.org/W3018121029","https://openalex.org/W3021994024","https://openalex.org/W3022690656","https://openalex.org/W3025333324","https://openalex.org/W3033730550","https://openalex.org/W3034117989","https://openalex.org/W3037021529","https://openalex.org/W3083628850","https://openalex.org/W3087372838","https://openalex.org/W3094601437","https://openalex.org/W3105447427","https://openalex.org/W3111890416","https://openalex.org/W3119014068","https://openalex.org/W3119844389","https://openalex.org/W3122492245","https://openalex.org/W3130192503","https://openalex.org/W3130291956","https://openalex.org/W3131627768","https://openalex.org/W3134538779","https://openalex.org/W3135597500","https://openalex.org/W3164622462","https://openalex.org/W6779071719","https://openalex.org/W6788906148"],"related_works":["https://openalex.org/W2093589470","https://openalex.org/W2415751681","https://openalex.org/W1862394037","https://openalex.org/W2889925888","https://openalex.org/W3121271574","https://openalex.org/W4205160129","https://openalex.org/W2084594947","https://openalex.org/W2890995276","https://openalex.org/W4381804751","https://openalex.org/W2076258781"],"abstract_inverted_index":{"Complexity":[0],"analysis":[1,31,39,217],"of":[2,18,28,40,69,93,99,136,171,184,194,207,215,221,228],"fractional-order":[3,19,42,138,185,208],"chaotic":[4,20,43,139,186,209,223],"system":[5,21,44,140,187,224],"is":[6,25,64,101,141,173,188],"an":[7],"interesting":[8],"topic":[9],"in":[10,180,225],"recent":[11],"years.":[12],"How":[13],"to":[14,83],"measure":[15],"the":[16,26,67,91,97,104,119,123,130,134,148,155,169,174,177,181,192,195,205,213,226],"complexity":[17,38,86,100,135,150,193,206],"correctly":[22],"and":[23,32,57,79,113,116,146,154,176,211,218,236],"effectively":[24],"basis":[27,214],"its":[29],"theoretical":[30,216],"engineering":[33],"application.":[34],"In":[35,66,90],"this":[36],"paper,":[37],"three-dimensional":[41,137],"based":[45],"on":[46],"multivariate":[47,52,58],"multiscale":[48,53,59],"fuzzy":[49],"entropy":[50,55,61,74],"(mvMFE),":[51],"sample":[54],"(mvMSE)":[56],"dispersion":[60],"(mvMDE)":[62],"respectively":[63],"proposed.":[65],"case":[68,92],"single":[70,152],"parameter":[71,153],"change,":[72,96],"different":[73],"such":[75],"as":[76,110,118,163],"mvMFE,":[77,114,144],"mvMSE":[78],"mvMDE":[80,117,172],"are":[81,161],"used":[82,162],"analyze":[84],"how":[85],"varies":[87],"with":[88,191],"parameter.":[89],"two":[94,108,124,159],"parameters":[95,109,125,160],"change":[98,126],"analyzed":[102,142],"by":[103,143],"chromatomap":[105],"which":[106],"takes":[107],"independent":[111],"variable,":[112],"mvMSE,":[115,145],"dependent":[120],"variable":[121],"when":[122,133],"simultaneously.":[127],"Aiming":[128],"at":[129],"performance":[131,170],"problem":[132],"mvMDE,":[147],"maximum":[149],"under":[151,158],"detection":[156],"area":[157],"indicators.":[164],"The":[165],"result":[166],"shows":[167],"that":[168],"best,":[175],"nonlinear":[178],"term":[179],"mathematical":[182],"model":[183],"positively":[189],"correlated":[190],"system.":[196],"This":[197],"will":[198],"provide":[199],"a":[200],"new":[201],"method":[202],"for":[203],"measuring":[204],"system,":[210],"lay":[212],"practical":[219],"application":[220],"fractional":[222],"fields":[227],"image":[229,233],"encryption,":[230,232],"sound":[231],"compression-encryption":[234],"technique,":[235],"secure":[237],"communication.":[238]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}