{"id":"https://openalex.org/W3172821497","doi":"https://doi.org/10.3390/sym13061047","title":"A 2D Hyperchaotic Map: Amplitude Control, Coexisting Symmetrical Attractors and Circuit Implementation","display_name":"A 2D Hyperchaotic Map: Amplitude Control, Coexisting Symmetrical Attractors and Circuit Implementation","publication_year":2021,"publication_date":"2021-06-10","ids":{"openalex":"https://openalex.org/W3172821497","doi":"https://doi.org/10.3390/sym13061047","mag":"3172821497"},"language":"en","primary_location":{"id":"doi:10.3390/sym13061047","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061047","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1047/pdf?version=1623305646","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/2073-8994/13/6/1047/pdf?version=1623305646","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090100824","display_name":"Xuejiao Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuejiao Zhou","raw_affiliation_strings":["Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China"],"affiliations":[{"raw_affiliation_string":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031215480","display_name":"Chunbiao Li","orcid":"https://orcid.org/0000-0002-9932-0914"},"institutions":[{"id":"https://openalex.org/I152269853","display_name":"Qilu University of Technology","ror":"https://ror.org/04hyzq608","country_code":"CN","type":"education","lineage":["https://openalex.org/I152269853"]},{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chunbiao Li","raw_affiliation_strings":["Collaborative Innovation Center of Memristive Computing Application (CICMCA), Qilu Institute of Technology, Jinan 250200, China","Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China","School of Artificial Intelligence, Nanjing University of Information Science & Technology, Nanjing 210044, China"],"affiliations":[{"raw_affiliation_string":"Collaborative Innovation Center of Memristive Computing Application (CICMCA), Qilu Institute of Technology, Jinan 250200, China","institution_ids":["https://openalex.org/I152269853"]},{"raw_affiliation_string":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]},{"raw_affiliation_string":"School of Artificial Intelligence, Nanjing University of Information Science & Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030187165","display_name":"Xu Lu","orcid":"https://orcid.org/0000-0001-8786-2831"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu Lu","raw_affiliation_strings":["Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China"],"affiliations":[{"raw_affiliation_string":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065761469","display_name":"Tengfei Lei","orcid":"https://orcid.org/0000-0001-5243-1046"},"institutions":[{"id":"https://openalex.org/I152269853","display_name":"Qilu University of Technology","ror":"https://ror.org/04hyzq608","country_code":"CN","type":"education","lineage":["https://openalex.org/I152269853"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tengfei Lei","raw_affiliation_strings":["Collaborative Innovation Center of Memristive Computing Application (CICMCA), Qilu Institute of Technology, Jinan 250200, China"],"affiliations":[{"raw_affiliation_string":"Collaborative Innovation Center of Memristive Computing Application (CICMCA), Qilu Institute of Technology, Jinan 250200, China","institution_ids":["https://openalex.org/I152269853"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113985571","display_name":"Yibo Zhao","orcid":"https://orcid.org/0009-0008-3584-4592"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yibo Zhao","raw_affiliation_strings":["Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China"],"affiliations":[{"raw_affiliation_string":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5031215480"],"corresponding_institution_ids":["https://openalex.org/I152269853","https://openalex.org/I200845125"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.1818,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.78423997,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"13","issue":"6","first_page":"1047","last_page":"1047"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9976999759674072,"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":0.9976999759674072,"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":0.9951000213623047,"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/T10320","display_name":"Neural Networks and Applications","score":0.9368000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.8675719499588013},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.8134441375732422},{"id":"https://openalex.org/keywords/polarity","display_name":"Polarity (international relations)","score":0.5908976793289185},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5839477777481079},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5402374863624573},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4804943799972534},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.4523237645626068},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.44657084345817566},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.433494508266449},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39539796113967896},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.322085440158844},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31032443046569824},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.25924795866012573},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07629695534706116},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.07518044114112854},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0709494948387146},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0702035129070282}],"concepts":[{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.8675719499588013},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8134441375732422},{"id":"https://openalex.org/C2777361361","wikidata":"https://www.wikidata.org/wiki/Q1112585","display_name":"Polarity (international relations)","level":3,"score":0.5908976793289185},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5839477777481079},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5402374863624573},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4804943799972534},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.4523237645626068},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.44657084345817566},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.433494508266449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39539796113967896},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.322085440158844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31032443046569824},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.25924795866012573},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07629695534706116},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.07518044114112854},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0709494948387146},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0702035129070282},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C1491633281","wikidata":"https://www.wikidata.org/wiki/Q7868","display_name":"Cell","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13061047","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061047","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1047/pdf?version=1623305646","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:28729c43928245eb910f8ff3ac82bbab","is_oa":true,"landing_page_url":"https://doaj.org/article/28729c43928245eb910f8ff3ac82bbab","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":"Symmetry, Vol 13, Iss 6, p 1047 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/6/1047/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13061047","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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13061047","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061047","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1047/pdf?version=1623305646","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/G1993483461","display_name":null,"funder_award_id":"61871230","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5889787216","display_name":null,"funder_award_id":"BK20181410","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3172821497.pdf","grobid_xml":"https://content.openalex.org/works/W3172821497.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W1656086158","https://openalex.org/W1976581203","https://openalex.org/W2061695646","https://openalex.org/W2092161052","https://openalex.org/W2140187929","https://openalex.org/W2146046397","https://openalex.org/W2513087591","https://openalex.org/W2528437065","https://openalex.org/W2592978607","https://openalex.org/W2743732015","https://openalex.org/W2746989737","https://openalex.org/W2748460474","https://openalex.org/W2776204315","https://openalex.org/W2795386454","https://openalex.org/W2903779703","https://openalex.org/W2916323064","https://openalex.org/W2964432840","https://openalex.org/W2982740292","https://openalex.org/W2990234538","https://openalex.org/W2997056246","https://openalex.org/W3006142668","https://openalex.org/W3009780791","https://openalex.org/W3010687946","https://openalex.org/W3013583552","https://openalex.org/W3014351659","https://openalex.org/W3014539624","https://openalex.org/W3014753608","https://openalex.org/W3022677734","https://openalex.org/W3029783782","https://openalex.org/W3037032721","https://openalex.org/W3081655872","https://openalex.org/W3088180343","https://openalex.org/W3089230651","https://openalex.org/W3123938732","https://openalex.org/W3126842306"],"related_works":["https://openalex.org/W3049714198","https://openalex.org/W2960434112","https://openalex.org/W2036805113","https://openalex.org/W2592279130","https://openalex.org/W1953967074","https://openalex.org/W2063428335","https://openalex.org/W2950588017","https://openalex.org/W2382985519","https://openalex.org/W1515854972","https://openalex.org/W1975913940"],"abstract_inverted_index":{"An":[0],"absolute":[1,19],"value":[2],"function":[3],"was":[4,12],"introduced":[5],"for":[6,24,82],"chaos":[7],"construction,":[8],"where":[9,40,87],"hyperchaotic":[10],"oscillation":[11],"found":[13],"with":[14,70,100],"amplitude":[15,25,30,36,88],"rescaling.":[16],"The":[17],"nonlinear":[18],"term":[20],"brings":[21],"the":[22,41,65,71,75],"convenience":[23],"control.":[26],"Two":[27],"regimes":[28],"of":[29,53],"control":[31,37,89],"including":[32],"total":[33],"and":[34,74,96],"partial":[35],"are":[38,56,103],"discussed,":[39],"attractor":[42],"can":[43],"be":[44],"rescaled":[45],"separately":[46],"by":[47,58,64],"two":[48],"independent":[49],"coefficients.":[50],"Symmetrical":[51],"pairs":[52],"coexisting":[54,97],"attractors":[55],"captured":[57],"corresponding":[59],"initial":[60],"conditions.":[61],"Circuit":[62],"implementation":[63],"platform":[66],"STM32":[67],"is":[68,80,90],"consistent":[69],"numerical":[72],"exploration":[73],"theoretical":[76],"observation.":[77],"This":[78],"finding":[79],"helpful":[81],"promoting":[83],"discrete":[84],"map":[85],"application,":[86],"realized":[91],"in":[92],"an":[93],"easy":[94],"way":[95],"symmetrical":[98],"sequences":[99],"opposite":[101],"polarity":[102],"obtained.":[104]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}