{"id":"https://openalex.org/W4383877109","doi":"https://doi.org/10.3390/sym15071398","title":"A Novel Fractional-Order Memristive Chaotic Circuit with Coexisting Double-Layout Four-Scroll Attractors and Its Application in Visually Meaningful Image Encryption","display_name":"A Novel Fractional-Order Memristive Chaotic Circuit with Coexisting Double-Layout Four-Scroll Attractors and Its Application in Visually Meaningful Image Encryption","publication_year":2023,"publication_date":"2023-07-11","ids":{"openalex":"https://openalex.org/W4383877109","doi":"https://doi.org/10.3390/sym15071398"},"language":"en","primary_location":{"id":"doi:10.3390/sym15071398","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15071398","pdf_url":"https://www.mdpi.com/2073-8994/15/7/1398/pdf?version=1689050105","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/7/1398/pdf?version=1689050105","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006298594","display_name":"Yuebo Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210147745","display_name":"West Anhui University","ror":"https://ror.org/046ft6c74","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147745"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuebo Wu","raw_affiliation_strings":["School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu\u2019an 237012, China","School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu'an 237012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu\u2019an 237012, China","institution_ids":["https://openalex.org/I4210147745"]},{"raw_affiliation_string":"School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu'an 237012, China","institution_ids":["https://openalex.org/I4210147745"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052513533","display_name":"Duansong Wang","orcid":"https://orcid.org/0000-0001-9523-3517"},"institutions":[{"id":"https://openalex.org/I4210147745","display_name":"West Anhui University","ror":"https://ror.org/046ft6c74","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147745"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Duansong Wang","raw_affiliation_strings":["School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu\u2019an 237012, China","School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu'an 237012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu\u2019an 237012, China","institution_ids":["https://openalex.org/I4210147745"]},{"raw_affiliation_string":"School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu'an 237012, China","institution_ids":["https://openalex.org/I4210147745"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100615714","display_name":"Tan Zhang","orcid":"https://orcid.org/0000-0002-6713-5036"},"institutions":[{"id":"https://openalex.org/I4210147745","display_name":"West Anhui University","ror":"https://ror.org/046ft6c74","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147745"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tan Zhang","raw_affiliation_strings":["School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu\u2019an 237012, China","School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu'an 237012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu\u2019an 237012, China","institution_ids":["https://openalex.org/I4210147745"]},{"raw_affiliation_string":"School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu'an 237012, China","institution_ids":["https://openalex.org/I4210147745"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063087053","display_name":"Jinzhong Zhang","orcid":"https://orcid.org/0000-0003-1511-4281"},"institutions":[{"id":"https://openalex.org/I4210147745","display_name":"West Anhui University","ror":"https://ror.org/046ft6c74","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147745"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinzhong Zhang","raw_affiliation_strings":["School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu\u2019an 237012, China","School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu'an 237012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu\u2019an 237012, China","institution_ids":["https://openalex.org/I4210147745"]},{"raw_affiliation_string":"School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu'an 237012, China","institution_ids":["https://openalex.org/I4210147745"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102908532","display_name":"Jian Zhou","orcid":"https://orcid.org/0000-0002-9672-7276"},"institutions":[{"id":"https://openalex.org/I4210147745","display_name":"West Anhui University","ror":"https://ror.org/046ft6c74","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147745"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jian Zhou","raw_affiliation_strings":["School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu\u2019an 237012, China","School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu'an 237012, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu\u2019an 237012, China","institution_ids":["https://openalex.org/I4210147745"]},{"raw_affiliation_string":"School of Electrical and Opto-Electronic Engineering, West Anhui University, Lu'an 237012, China","institution_ids":["https://openalex.org/I4210147745"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102908532"],"corresponding_institution_ids":["https://openalex.org/I4210147745"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.2514,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.45197119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"15","issue":"7","first_page":"1398","last_page":"1398"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9968000054359436,"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":0.9871000051498413,"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/memristor","display_name":"Memristor","score":0.8355145454406738},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.7641814947128296},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6982402801513672},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.6573876738548279},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.6205859184265137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5391519069671631},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5333680510520935},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.5075277090072632},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5052292943000793},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.44430339336395264},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40235015749931335},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37596866488456726},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23068982362747192},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11700841784477234},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10685965418815613},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.09855839610099792},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07406947016716003}],"concepts":[{"id":"https://openalex.org/C150072547","wikidata":"https://www.wikidata.org/wiki/Q212923","display_name":"Memristor","level":2,"score":0.8355145454406738},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7641814947128296},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6982402801513672},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.6573876738548279},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.6205859184265137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5391519069671631},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5333680510520935},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.5075277090072632},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5052292943000793},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.44430339336395264},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40235015749931335},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37596866488456726},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23068982362747192},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11700841784477234},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10685965418815613},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.09855839610099792},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07406947016716003},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15071398","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15071398","pdf_url":"https://www.mdpi.com/2073-8994/15/7/1398/pdf?version=1689050105","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3e6148bec58e485289afbfd15bf57897","is_oa":false,"landing_page_url":"https://doaj.org/article/3e6148bec58e485289afbfd15bf57897","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 7, p 1398 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/7/1398/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15071398","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":"Symmetry; Volume 15; Issue 7; Pages: 1398","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15071398","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15071398","pdf_url":"https://www.mdpi.com/2073-8994/15/7/1398/pdf?version=1689050105","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2631072990","display_name":null,"funder_award_id":"WGKQ2021050","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"},{"id":"https://openalex.org/G9598557","display_name":null,"funder_award_id":"2008085MA20","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"}],"funders":[{"id":"https://openalex.org/F4320321435","display_name":"Anhui University","ror":"https://ror.org/05th6yx34"},{"id":"https://openalex.org/F4320330928","display_name":"West Anhui University","ror":"https://ror.org/046ft6c74"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4383877109.pdf"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W184169697","https://openalex.org/W844411675","https://openalex.org/W1528987510","https://openalex.org/W1972926236","https://openalex.org/W1975229527","https://openalex.org/W2018341541","https://openalex.org/W2095360730","https://openalex.org/W2112181056","https://openalex.org/W2133665775","https://openalex.org/W2162651880","https://openalex.org/W2346614146","https://openalex.org/W2551769760","https://openalex.org/W2606645644","https://openalex.org/W2805246418","https://openalex.org/W2895660505","https://openalex.org/W2899381968","https://openalex.org/W2907873451","https://openalex.org/W2944931886","https://openalex.org/W3001781461","https://openalex.org/W3014798532","https://openalex.org/W3023762473","https://openalex.org/W3025598099","https://openalex.org/W3090224803","https://openalex.org/W3098618696","https://openalex.org/W3122214732","https://openalex.org/W3129410382","https://openalex.org/W3139361157","https://openalex.org/W3165637542","https://openalex.org/W3194200542","https://openalex.org/W3194395762","https://openalex.org/W3201868523","https://openalex.org/W3217786002","https://openalex.org/W4200233568","https://openalex.org/W4220654448","https://openalex.org/W4221045263","https://openalex.org/W4226495087","https://openalex.org/W4282826758","https://openalex.org/W4283164029","https://openalex.org/W4288735490","https://openalex.org/W4295132041","https://openalex.org/W4311728823","https://openalex.org/W6796103704","https://openalex.org/W6800577433"],"related_works":["https://openalex.org/W2391540797","https://openalex.org/W4206623065","https://openalex.org/W2005355485","https://openalex.org/W1570727143","https://openalex.org/W168375694","https://openalex.org/W2703435152","https://openalex.org/W2119092717","https://openalex.org/W2063555990","https://openalex.org/W2002820797","https://openalex.org/W3153461053"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,8,32,123],"fractional-order":[4,81],"chaotic":[5,43,83],"system":[6,27,84,106,133],"using":[7],"tri-stable":[9],"locally":[10,64],"active":[11],"memristor.":[12],"The":[13],"characteristics":[14],"of":[15,20,24,56,73,79,90,103,152,159],"the":[16,25,42,53,57,69,80,88,95,104,110,131,150,153,160],"memristor,":[17],"dynamic":[18,71],"mechanism":[19,72],"oscillation,":[21,74],"and":[22,30,47,66,77,87,101,109,117,136,144,156],"behaviors":[23],"proposed":[26,132,161],"were":[28,85,92,107],"analyzed,":[29],"then":[31],"visually":[33,124],"meaningful":[34,125],"image":[35,126,162],"encryption":[36,127,163],"scheme":[37,128],"was":[38,59,62,134,139],"designed":[39],"based":[40,129],"on":[41,119,130],"system,":[44],"DNA":[45],"encoding,":[46],"integer":[48],"wavelet":[49],"transform":[50],"(IWT).":[51],"Firstly,":[52],"mathematical":[54],"model":[55],"memristor":[58],"designed,":[60,135],"which":[61],"nonvolatile,":[63],"active,":[65],"tri-stable.":[67],"Secondly,":[68],"stability,":[70],"bifurcation":[75,99],"behaviors,":[76],"complexity":[78,102],"memristive":[82],"investigated":[86],"conditions":[89],"stability":[91],"obtained.":[93],"Thirdly,":[94],"largest":[96],"Lyapunov":[97],"exponent,":[98],"diagram,":[100],"novel":[105],"calculated":[108],"coexisting":[111,113],"bifurcation,":[112],"attractors,":[114],"spectral":[115],"entropy,":[116],"so":[118],"are":[120],"shown.":[121],"Finally,":[122],"its":[137],"security":[138,158],"assessed":[140],"by":[141],"statistical":[142],"analysis":[143,155],"different":[145],"attacks.":[146],"Numerical":[147],"simulation":[148],"demonstrated":[149],"effectiveness":[151],"theoretical":[154],"high":[157],"scheme.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2023-07-12T00:00:00"}
