{"id":"https://openalex.org/W4282942835","doi":"https://doi.org/10.1142/s021812742250095x","title":"Constructing a 3D Exponential Hyperchaotic Map with Application to PRNG","display_name":"Constructing a 3D Exponential Hyperchaotic Map with Application to PRNG","publication_year":2022,"publication_date":"2022-06-10","ids":{"openalex":"https://openalex.org/W4282942835","doi":"https://doi.org/10.1142/s021812742250095x"},"language":"en","primary_location":{"id":"doi:10.1142/s021812742250095x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812742250095x","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/A5045578837","display_name":"Yuanyuan Si","orcid":"https://orcid.org/0000-0003-0809-2424"},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanyuan Si","raw_affiliation_strings":["School of Mathematical Sciences, University of Jinan, Jinan 250022, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Jinan, Jinan 250022, P. R. China","institution_ids":["https://openalex.org/I34949971"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084387750","display_name":"Hongjun Liu","orcid":"https://orcid.org/0000-0003-4991-6696"},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongjun Liu","raw_affiliation_strings":["School of Mathematical Sciences, University of Jinan, Jinan 250022, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Jinan, Jinan 250022, P. R. China","institution_ids":["https://openalex.org/I34949971"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036479222","display_name":"Yuehui Chen","orcid":"https://orcid.org/0000-0002-5265-903X"},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuehui Chen","raw_affiliation_strings":["School of Information Science and Engineering, University of Jinan, Jinan 250022, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, University of Jinan, Jinan 250022, P. R. China","institution_ids":["https://openalex.org/I34949971"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084387750"],"corresponding_institution_ids":["https://openalex.org/I34949971"],"apc_list":null,"apc_paid":null,"fwci":3.9766,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.94979095,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"32","issue":"07","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9998000264167786,"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":0.9998000264167786,"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/T10244","display_name":"Chaos control and synchronization","score":0.9965000152587891,"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9843000173568726,"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/ergodicity","display_name":"Ergodicity","score":0.7696976661682129},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7288268804550171},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6558999419212341},{"id":"https://openalex.org/keywords/aperiodic-graph","display_name":"Aperiodic graph","score":0.5933729410171509},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.5704869627952576},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.552362859249115},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5215880274772644},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4610627591609955},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.45149821043014526},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4383937418460846},{"id":"https://openalex.org/keywords/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.41795504093170166},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33006471395492554},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28397488594055176},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25429823994636536},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2337702512741089},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13766294717788696},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1078760027885437},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08436256647109985}],"concepts":[{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.7696976661682129},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7288268804550171},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6558999419212341},{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.5933729410171509},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.5704869627952576},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.552362859249115},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5215880274772644},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4610627591609955},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45149821043014526},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4383937418460846},{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.41795504093170166},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33006471395492554},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28397488594055176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25429823994636536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2337702512741089},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13766294717788696},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1078760027885437},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08436256647109985},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/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/s021812742250095x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812742250095x","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":[{"id":"https://openalex.org/G4042762610","display_name":null,"funder_award_id":"61662073","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1862394037","https://openalex.org/W2068684969","https://openalex.org/W2087094626","https://openalex.org/W2344050291","https://openalex.org/W2533312261","https://openalex.org/W2567775486","https://openalex.org/W2760188900","https://openalex.org/W2790533449","https://openalex.org/W2905309958","https://openalex.org/W2905741893","https://openalex.org/W2944962845","https://openalex.org/W2951356163","https://openalex.org/W2952052242","https://openalex.org/W2952974476","https://openalex.org/W2985012163","https://openalex.org/W2999435040","https://openalex.org/W3005341457","https://openalex.org/W3012385585","https://openalex.org/W3082459396","https://openalex.org/W3091991102","https://openalex.org/W3094970337","https://openalex.org/W3115910882","https://openalex.org/W3120522579","https://openalex.org/W3127459604","https://openalex.org/W3165742426","https://openalex.org/W3170049569"],"related_works":["https://openalex.org/W2037661079","https://openalex.org/W2339191433","https://openalex.org/W1992569127","https://openalex.org/W4220811941","https://openalex.org/W1609792066","https://openalex.org/W2795569938","https://openalex.org/W61644174","https://openalex.org/W2383239787","https://openalex.org/W95325373","https://openalex.org/W2166239524"],"abstract_inverted_index":{"Some":[0],"weaknesses":[1],"of":[2,9,85],"1D":[3,38],"chaotic":[4,28],"maps,":[5],"such":[6,53],"as":[7,54],"lacking":[8],"ergodicity,":[10],"multiple":[11],"bifurcations,":[12],"dense":[13],"periodic":[14,108],"windows,":[15],"and":[16,49,67,71,88,100,111,123],"short":[17],"iteration":[18],"period,":[19],"limit":[20],"their":[21],"practical":[22],"applications":[23],"in":[24,81],"cryptography.":[25],"A":[26],"higher-dimensional":[27],"map":[29,45],"with":[30],"ergodicity":[31,80],"can":[32,131],"solve":[33],"these":[34],"problems.":[35],"Based":[36],"on":[37],"quadratic":[39],"map,":[40],"a":[41,82,93,105,128],"3D":[42],"exponential":[43],"hyperchaotic":[44],"(3D-EHCM)":[46],"is":[47],"constructed,":[48],"its":[50,89],"dynamic":[51],"behaviors,":[52],"phase":[55],"diagram,":[56],"Lyapunov":[57],"exponent":[58],"spectrum,":[59],"Kolmogorov":[60],"entropy":[61,66],"(KE),":[62],"correlation":[63],"dimension,":[64],"approximate":[65],"randomness,":[68],"are":[69,115],"analyzed":[70],"tested.":[72],"The":[73],"results":[74,125],"demonstrate":[75,126],"that":[76,127],"the":[77,107,119],"3D-EHCM":[78],"has":[79],"larger":[83],"range":[84],"control":[86],"parameter,":[87],"state":[90],"points":[91],"have":[92],"longer":[94],"period.":[95],"To":[96],"counteract":[97],"dynamical":[98],"degradation":[99],"make":[101],"it":[102],"suitable":[103],"for":[104],"PRNG,":[106],"point":[109],"detection":[110],"random":[112],"impulsive":[113],"perturbation":[114],"applied":[116],"to":[117],"lengthen":[118],"aperiodic":[120],"time":[121],"sequence,":[122],"statistical":[124],"full-period":[129],"sequence":[130],"be":[132],"obtained.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":21},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}