{"id":"https://openalex.org/W3036241369","doi":"https://doi.org/10.3390/e22060671","title":"Chaos Control and Synchronization of a Complex Rikitake Dynamo Model","display_name":"Chaos Control and Synchronization of a Complex Rikitake Dynamo Model","publication_year":2020,"publication_date":"2020-06-17","ids":{"openalex":"https://openalex.org/W3036241369","doi":"https://doi.org/10.3390/e22060671","mag":"3036241369","pmid":"https://pubmed.ncbi.nlm.nih.gov/33286443"},"language":"en","primary_location":{"id":"doi:10.3390/e22060671","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22060671","pdf_url":"https://www.mdpi.com/1099-4300/22/6/671/pdf","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://www.mdpi.com/1099-4300/22/6/671/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059279222","display_name":"Wenkai Pang","orcid":null},"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/I4210142748","display_name":"Shandong Academy of Sciences","ror":"https://ror.org/04y8d6y55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenkai Pang","raw_affiliation_strings":["School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China","institution_ids":["https://openalex.org/I4210142748","https://openalex.org/I152269853"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061884630","display_name":"Zekang Wu","orcid":null},"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/I4210142748","display_name":"Shandong Academy of Sciences","ror":"https://ror.org/04y8d6y55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zekang Wu","raw_affiliation_strings":["School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China","institution_ids":["https://openalex.org/I4210142748","https://openalex.org/I152269853"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101786440","display_name":"Yu Xiao","orcid":"https://orcid.org/0000-0001-6789-4262"},"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/I4210142748","display_name":"Shandong Academy of Sciences","ror":"https://ror.org/04y8d6y55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu Xiao","raw_affiliation_strings":["School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China","institution_ids":["https://openalex.org/I4210142748","https://openalex.org/I152269853"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101531054","display_name":"Cuimei Jiang","orcid":"https://orcid.org/0000-0002-1032-8355"},"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/I4210142748","display_name":"Shandong Academy of Sciences","ror":"https://ror.org/04y8d6y55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cuimei Jiang","raw_affiliation_strings":["School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China","institution_ids":["https://openalex.org/I4210142748","https://openalex.org/I152269853"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101531054"],"corresponding_institution_ids":["https://openalex.org/I152269853","https://openalex.org/I4210142748"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6675,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.67432346,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"22","issue":"6","first_page":"671","last_page":"671"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9995999932289124,"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":0.9995999932289124,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9922999739646912,"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/control-theory","display_name":"Control theory (sociology)","score":0.6085036396980286},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6041204929351807},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5903419852256775},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.5863133072853088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5467513799667358},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5343847274780273},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4837384521961212},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.47776710987091064},{"id":"https://openalex.org/keywords/chaos","display_name":"CHAOS (operating system)","score":0.45312926173210144},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41937345266342163},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.366102933883667},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.23271146416664124},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.17978990077972412},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.1618574559688568},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1460379660129547},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.128351628780365}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6085036396980286},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6041204929351807},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5903419852256775},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.5863133072853088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5467513799667358},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5343847274780273},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4837384521961212},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.47776710987091064},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.45312926173210144},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41937345266342163},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.366102933883667},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.23271146416664124},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.17978990077972412},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.1618574559688568},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1460379660129547},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.128351628780365},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e22060671","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22060671","pdf_url":"https://www.mdpi.com/1099-4300/22/6/671/pdf","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:33286443","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33286443","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:0d69a4d9f3bf476abdfc02ae44e549a0","is_oa":true,"landing_page_url":"https://doaj.org/article/0d69a4d9f3bf476abdfc02ae44e549a0","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 22, Iss 6, p 671 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/22/6/671/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e22060671","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":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7517210","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7517210","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/e22060671","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22060671","pdf_url":"https://www.mdpi.com/1099-4300/22/6/671/pdf","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3036241369.pdf","grobid_xml":"https://content.openalex.org/works/W3036241369.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W583670360","https://openalex.org/W1546375104","https://openalex.org/W1970442252","https://openalex.org/W1978878677","https://openalex.org/W2001208819","https://openalex.org/W2008063885","https://openalex.org/W2009076302","https://openalex.org/W2018522871","https://openalex.org/W2024694830","https://openalex.org/W2031970152","https://openalex.org/W2050561628","https://openalex.org/W2087414632","https://openalex.org/W2093579835","https://openalex.org/W2098659599","https://openalex.org/W2118162106","https://openalex.org/W2140422080","https://openalex.org/W2145069124","https://openalex.org/W2146851929","https://openalex.org/W2162144003","https://openalex.org/W2331522519","https://openalex.org/W2432419794","https://openalex.org/W2588335543","https://openalex.org/W2743316136","https://openalex.org/W2744196846","https://openalex.org/W2753121411","https://openalex.org/W2781177099","https://openalex.org/W2793662887","https://openalex.org/W2897131960","https://openalex.org/W2898961287","https://openalex.org/W2944962845","https://openalex.org/W2982314864","https://openalex.org/W2982509241","https://openalex.org/W4251015067","https://openalex.org/W6652532437","https://openalex.org/W6702386150","https://openalex.org/W6762541141"],"related_works":["https://openalex.org/W1979229270","https://openalex.org/W2374600121","https://openalex.org/W2027784897","https://openalex.org/W125502673","https://openalex.org/W2384948345","https://openalex.org/W2019045751","https://openalex.org/W2776265842","https://openalex.org/W2361515791","https://openalex.org/W2375956839","https://openalex.org/W2899627504"],"abstract_inverted_index":{"A":[0],"novel":[1],"chaotic":[2],"system":[3,7,42,68],"called":[4],"complex":[5,40,66],"Rikitake":[6,41,67],"is":[8],"proposed.":[9],"Dynamical":[10],"properties,":[11],"including":[12],"symmetry,":[13],"dissipation,":[14],"stability":[15],"of":[16,27,58,61],"equilibria,":[17],"Lyapunov":[18],"exponents":[19],"and":[20,30],"bifurcation,":[21],"are":[22,80],"analyzed":[23],"on":[24,35],"the":[25,39,56,65],"basis":[26],"theoretical":[28],"analysis":[29],"numerical":[31,83],"simulation.":[32],"Further,":[33],"based":[34],"feedback":[36],"control":[37],"method,":[38],"can":[43],"be":[44],"controlled":[45],"to":[46,74],"any":[47],"equilibrium":[48],"points.":[49],"Additionally,":[50],"this":[51],"paper":[52],"not":[53],"only":[54],"proves":[55],"existence":[57],"two":[59],"types":[60],"synchronization":[62],"schemes":[63],"in":[64],"but":[69],"also":[70],"designs":[71],"adaptive":[72],"controllers":[73],"realize":[75],"them.":[76],"The":[77],"proposed":[78],"results":[79],"verified":[81],"by":[82],"simulations.":[84]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
