{"id":"https://openalex.org/W7131796767","doi":"https://doi.org/10.3390/e28030260","title":"Analysis and Application of a 3D Chaotic System with Flexible Offset and Frequency Control","display_name":"Analysis and Application of a 3D Chaotic System with Flexible Offset and Frequency Control","publication_year":2026,"publication_date":"2026-02-27","ids":{"openalex":"https://openalex.org/W7131796767","doi":"https://doi.org/10.3390/e28030260","pmid":"https://pubmed.ncbi.nlm.nih.gov/41899912"},"language":"en","primary_location":{"id":"doi:10.3390/e28030260","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030260","pdf_url":null,"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","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/e28030260","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122032766","display_name":"Shuaishuai Shi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shuaishuai Shi","raw_affiliation_strings":["School of Information Engineering, Guizhou University of Engineering Science, Bijie 551700, China"],"raw_orcid":"https://orcid.org/0009-0008-1530-6535","affiliations":[{"raw_affiliation_string":"School of Information Engineering, Guizhou University of Engineering Science, Bijie 551700, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126967865","display_name":"Jiangfan Xiong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiangfan Xiong","raw_affiliation_strings":["School of Information Engineering, Guizhou University of Engineering Science, Bijie 551700, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Engineering, Guizhou University of Engineering Science, Bijie 551700, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019799825","display_name":"Licai Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090773","display_name":"Anshun University","ror":"https://ror.org/009jy0c86","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210090773"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Licai Liu","raw_affiliation_strings":["College of Electronics and Information Engineering, Anshun University, Anshun 561000, China"],"raw_orcid":"https://orcid.org/0000-0003-3399-2117","affiliations":[{"raw_affiliation_string":"College of Electronics and Information Engineering, Anshun University, Anshun 561000, China","institution_ids":["https://openalex.org/I4210090773"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5126963444","display_name":"Chuanhong Du","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090773","display_name":"Anshun University","ror":"https://ror.org/009jy0c86","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210090773"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuanhong Du","raw_affiliation_strings":["College of Electronics and Information Engineering, Anshun University, Anshun 561000, China"],"raw_orcid":"https://orcid.org/0000-0003-1568-9464","affiliations":[{"raw_affiliation_string":"College of Electronics and Information Engineering, Anshun University, Anshun 561000, China","institution_ids":["https://openalex.org/I4210090773"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5122032766"],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.34989503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"3","first_page":"260","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9718000292778015,"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":0.9718000292778015,"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":0.016699999570846558,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.0010999999940395355,"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/chaotic","display_name":"Chaotic","score":0.7275999784469604},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.642799973487854},{"id":"https://openalex.org/keywords/offset","display_name":"Offset (computer science)","score":0.5717999935150146},{"id":"https://openalex.org/keywords/frequency-offset","display_name":"Frequency offset","score":0.4853000044822693},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.4674000144004822},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.4499000012874603},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4498000144958496},{"id":"https://openalex.org/keywords/boosting","display_name":"Boosting (machine learning)","score":0.3752000033855438}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7275999784469604},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.642799973487854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6389999985694885},{"id":"https://openalex.org/C175291020","wikidata":"https://www.wikidata.org/wiki/Q1156822","display_name":"Offset (computer science)","level":2,"score":0.5717999935150146},{"id":"https://openalex.org/C49319798","wikidata":"https://www.wikidata.org/wiki/Q5502874","display_name":"Frequency offset","level":4,"score":0.4853000044822693},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.4674000144004822},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.4499000012874603},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4498000144958496},{"id":"https://openalex.org/C46686674","wikidata":"https://www.wikidata.org/wiki/Q466303","display_name":"Boosting (machine learning)","level":2,"score":0.3752000033855438},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.32670000195503235},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.32089999318122864},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.301800012588501},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.2529999911785126},{"id":"https://openalex.org/C88682704","wikidata":"https://www.wikidata.org/wiki/Q2907415","display_name":"DC bias","level":3,"score":0.25040000677108765}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e28030260","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030260","pdf_url":null,"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":"pmid:41899912","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41899912","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:572ad9e0352e48a3a79a6e947da63a4c","is_oa":true,"landing_page_url":"https://doaj.org/article/572ad9e0352e48a3a79a6e947da63a4c","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 28, Iss 3, p 260 (2026)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13025323","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13025323/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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 (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e28030260","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030260","pdf_url":null,"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W2069436097","https://openalex.org/W2667626071","https://openalex.org/W2775599534","https://openalex.org/W2912883855","https://openalex.org/W2915403258","https://openalex.org/W2976308763","https://openalex.org/W3169588883","https://openalex.org/W3186930505","https://openalex.org/W3207192273","https://openalex.org/W4308350141","https://openalex.org/W4318215146","https://openalex.org/W4377984325","https://openalex.org/W4378839907","https://openalex.org/W4386524465","https://openalex.org/W4387993099","https://openalex.org/W4388818897","https://openalex.org/W4390517532","https://openalex.org/W4400611639","https://openalex.org/W4401381050","https://openalex.org/W4402348870","https://openalex.org/W4405535967","https://openalex.org/W4406126273","https://openalex.org/W4406347594","https://openalex.org/W4406782414","https://openalex.org/W4406884638","https://openalex.org/W4408095071","https://openalex.org/W4408501381","https://openalex.org/W4408774185","https://openalex.org/W4408971077","https://openalex.org/W4409164704","https://openalex.org/W4409371667","https://openalex.org/W4410197126","https://openalex.org/W4410204036","https://openalex.org/W4410771999","https://openalex.org/W4411511771","https://openalex.org/W4413479126","https://openalex.org/W4413521821","https://openalex.org/W4416417298","https://openalex.org/W4417056635","https://openalex.org/W7115676323","https://openalex.org/W7118086725","https://openalex.org/W7119001730"],"related_works":[],"abstract_inverted_index":{"Signals":[0],"with":[1,22,89,121,197,245],"flexible":[2,23,118],"control":[3,106,120,146,240],"over":[4],"polarity":[5],"and":[6,14,49,84,154,166,200,235,254,263],"frequency":[7,122],"provide":[8],"an":[9,177],"essential":[10],"foundation":[11,265],"for":[12,231,266],"reliable":[13],"high-speed":[15],"information":[16],"transmission.":[17],"To":[18,140,220],"generate":[19],"chaotic":[20,31,45,72,114,135,175,195,243,270],"signals":[21],"output":[24],"characteristics":[25],"in":[26,92,126,133,157,205,272],"low-dimensional":[27],"systems,":[28,237],"a":[29,38,96,143,226],"novel":[30],"system":[32,56,80,150,159,193,244,271],"model":[33,180],"is":[34,57,124,152,161],"proposed":[35,79],"by":[36],"introducing":[37],"nonlinear":[39],"term":[40],"into":[41],"the":[42,55,78,107,134,173,184,192,214,218,223,233,242,261,268],"classical":[43],"Chen":[44],"system.":[46,219],"Dynamical":[47],"analysis":[48],"MATLAB":[50],"numerical":[51],"simulations":[52,75],"show":[53],"that":[54,77,191],"not":[58],"only":[59],"highly":[60],"sensitive":[61],"to":[62,148],"initial":[63],"conditions":[64],"but":[65],"also":[66],"capable":[67],"of":[68,109,217,241],"generating":[69],"three":[70,246],"distinct":[71,198],"attractors.":[73],"Further":[74],"confirm":[76,190],"demonstrates":[81,201],"arbitrary":[82,101,206],"unidirectional":[83],"multidirectional":[85],"offset":[86,90,102,119,202,247],"boosting":[87,203],"behaviors,":[88],"amplitudes":[91],"all":[93,110],"directions":[94],"having":[95],"wide":[97],"adjustable":[98],"range.":[99],"Furthermore,":[100],"constants":[103,147],"can":[104],"effectively":[105],"frequencies":[108],"state":[111],"variables.":[112],"This":[113],"system,":[115,176],"which":[116],"combines":[117],"regulation,":[123],"rare":[125],"existing":[127],"research.":[128],"Additionally,":[129,208],"certain":[130],"parameter":[131],"ranges":[132],"regime":[136],"are":[137],"relatively":[138],"narrow.":[139],"address":[141],"this,":[142,251],"method":[144],"involving":[145],"enhance":[149],"complexity":[151,160],"proposed,":[153],"its":[155],"effectiveness":[156],"increasing":[158],"validated":[162],"through":[163],"Lyapunov":[164],"spectrum":[165],"spectral":[167],"entropy":[168],"(SE)":[169],"analysis.":[170],"Based":[171,249],"on":[172,250],"constructed":[174],"equivalent":[178],"circuit":[179],"was":[181,229],"built":[182],"using":[183],"Multisim":[185],"14.0":[186],"platform.":[187],"Experimental":[188],"results":[189],"generates":[194],"attractors":[196],"structures":[199],"behavior":[204],"directions.":[207],"DSP":[209],"hardware":[210],"experiments":[211,256],"further":[212,259],"validate":[213],"physical":[215],"realizability":[216],"fully":[221],"exploit":[222],"system's":[224],"advantages,":[225],"synchronization":[227,239],"controller":[228],"designed":[230],"both":[232],"drive":[234],"response":[236],"enabling":[238],"constants.":[248],"data":[252],"encryption":[253],"transmission":[255],"were":[257],"conducted,":[258],"establishing":[260],"theoretical":[262],"experimental":[264],"applying":[267],"new":[269],"secure":[273],"communication.":[274]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-02-27T00:00:00"}