{"id":"https://openalex.org/W3000897954","doi":"https://doi.org/10.1155/2020/3085036","title":"Fractal Control and Synchronization of the Discrete Fractional SIRS Model","display_name":"Fractal Control and Synchronization of the Discrete Fractional SIRS Model","publication_year":2020,"publication_date":"2020-01-20","ids":{"openalex":"https://openalex.org/W3000897954","doi":"https://doi.org/10.1155/2020/3085036","mag":"3000897954"},"language":"en","primary_location":{"id":"doi:10.1155/2020/3085036","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/3085036","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/3085036.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2020/3085036.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086971421","display_name":"Miao Ouyang","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Miao Ouyang","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100714504","display_name":"Yongping Zhang","orcid":"https://orcid.org/0000-0002-8112-830X"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongping Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100414623","display_name":"Jian Liu","orcid":"https://orcid.org/0000-0001-7484-401X"},"institutions":[{"id":"https://openalex.org/I59483232","display_name":"Shandong University of Finance and Economics","ror":"https://ror.org/02e2nnq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I59483232"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Liu","raw_affiliation_strings":["School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China","institution_ids":["https://openalex.org/I59483232"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100714504"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.2664,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.50091344,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9973999857902527,"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":0.9973999857902527,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.6784237027168274},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.669830858707428},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6277011632919312},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.6145261526107788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5085145235061646},{"id":"https://openalex.org/keywords/julia-set","display_name":"Julia set","score":0.4759601950645447},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45755138993263245},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.42399922013282776},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4204522669315338},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4029552638530731},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40222129225730896},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28332242369651794},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2631057798862457},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2199995517730713},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.20002302527427673},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08296075463294983},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07587894797325134}],"concepts":[{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.6784237027168274},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.669830858707428},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6277011632919312},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6145261526107788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5085145235061646},{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.4759601950645447},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45755138993263245},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.42399922013282776},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4204522669315338},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4029552638530731},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40222129225730896},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28332242369651794},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2631057798862457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2199995517730713},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.20002302527427673},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08296075463294983},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07587894797325134},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2020/3085036","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/3085036","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/3085036.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:3085036","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2020/3085036.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:9bc503280c3842dfaba30643bf573760","is_oa":true,"landing_page_url":"https://doaj.org/article/9bc503280c3842dfaba30643bf573760","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":"Complexity, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/3085036","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/3085036","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/3085036.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","score":0.4300000071525574,"display_name":"Good health and well-being"}],"awards":[{"id":"https://openalex.org/G1336027239","display_name":null,"funder_award_id":"2019ZRJC005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1973267165","display_name":null,"funder_award_id":"61533011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1986336614","display_name":null,"funder_award_id":"U1806203","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2376276132","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2696157397","display_name":null,"funder_award_id":"ZR201","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G2784193076","display_name":null,"funder_award_id":"ZR2019MA051","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3238016531","display_name":null,"funder_award_id":"18062","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3289203325","display_name":null,"funder_award_id":"61533011","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G3296502557","display_name":null,"funder_award_id":"U1806203","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3497226477","display_name":null,"funder_award_id":"ZR2019","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4284476261","display_name":null,"funder_award_id":"2019ZRJC005","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7300980645","display_name":null,"funder_award_id":"2019ZRJC005","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G8498969030","display_name":null,"funder_award_id":"ZR2019MA051","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000897954.pdf","grobid_xml":"https://content.openalex.org/works/W3000897954.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W39945531","https://openalex.org/W1970416408","https://openalex.org/W1976461621","https://openalex.org/W1980337795","https://openalex.org/W1980466988","https://openalex.org/W1999216164","https://openalex.org/W2000368319","https://openalex.org/W2023035406","https://openalex.org/W2024667987","https://openalex.org/W2029197563","https://openalex.org/W2031064583","https://openalex.org/W2037545544","https://openalex.org/W2044063867","https://openalex.org/W2044803874","https://openalex.org/W2049931273","https://openalex.org/W2056565872","https://openalex.org/W2065126584","https://openalex.org/W2069095769","https://openalex.org/W2076743612","https://openalex.org/W2078282004","https://openalex.org/W2078434836","https://openalex.org/W2082493989","https://openalex.org/W2137133788","https://openalex.org/W2148016633","https://openalex.org/W2158629510","https://openalex.org/W2160754664","https://openalex.org/W2755270292","https://openalex.org/W2788851478","https://openalex.org/W2790258557","https://openalex.org/W2796056602","https://openalex.org/W2898999548","https://openalex.org/W2906690594","https://openalex.org/W2949001832","https://openalex.org/W2962729565"],"related_works":["https://openalex.org/W2169256438","https://openalex.org/W3022050839","https://openalex.org/W3016642159","https://openalex.org/W109862761","https://openalex.org/W4200163514","https://openalex.org/W2910981280","https://openalex.org/W3135283795","https://openalex.org/W4375959275","https://openalex.org/W4382753044","https://openalex.org/W4321499576"],"abstract_inverted_index":{"SIRS":[0,26],"model":[1,13],"is":[2,145],"one":[3],"of":[4,14,36,48,58,64,97,100,120,129,141],"the":[5,10,19,29,34,55,59,83,95,101,111,118,136,139,142,148],"most":[6],"basic":[7],"models":[8,27],"in":[9,82],"dynamic":[11],"warehouse":[12],"infectious":[15,50],"diseases,":[16],"which":[17,73],"describes":[18],"temporary":[20],"immunity":[21],"after":[22],"cure.":[23],"The":[24,125],"discrete":[25,102],"with":[28,106,110],"Caputo":[30],"deltas":[31],"sense":[32],"and":[33,39,45,79,127,138],"theories":[35],"fractional":[37,60,103],"calculus":[38],"fractal":[40],"theory":[41],"provide":[42],"a":[43,77,80],"reasonable":[44],"sensible":[46],"perspective":[47],"studying":[49],"disease":[51],"phenomenon.":[52],"After":[53],"discussing":[54],"fixed":[56,71],"point":[57],"order":[61,104],"system,":[62],"controllers":[63,90],"Julia":[65,98,121,130],"sets":[66,99,122,131],"are":[67,74,91,123],"designed":[68],"by":[69,147],"utilizing":[70],"point,":[72],"introduced":[75,92],"as":[76],"whole":[78],"part":[81],"models.":[84],"Then,":[85],"two":[86],"totally":[87],"different":[88,107],"coupled":[89],"to":[93],"achieve":[94],"synchronization":[96,119],"systems":[105],"parameters":[108],"but":[109],"same":[112],"structure.":[113],"And":[114],"new":[115],"proofs":[116],"about":[117],"given.":[124],"complexity":[126],"irregularity":[128],"can":[132],"be":[133],"seen":[134],"from":[135],"figures,":[137],"correctness":[140],"theoretical":[143],"analysis":[144],"exhibited":[146],"simulation":[149],"results.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
