{"id":"https://openalex.org/W4385740893","doi":"https://doi.org/10.3390/e25081192","title":"Stochastic Stabilization of Dual-Layer Rumor Propagation Model with Multiple Channels and Rumor-Detection Mechanism","display_name":"Stochastic Stabilization of Dual-Layer Rumor Propagation Model with Multiple Channels and Rumor-Detection Mechanism","publication_year":2023,"publication_date":"2023-08-10","ids":{"openalex":"https://openalex.org/W4385740893","doi":"https://doi.org/10.3390/e25081192","pmid":"https://pubmed.ncbi.nlm.nih.gov/37628221"},"language":"en","primary_location":{"id":"doi:10.3390/e25081192","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25081192","pdf_url":"https://www.mdpi.com/1099-4300/25/8/1192/pdf?version=1691716630","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/1099-4300/25/8/1192/pdf?version=1691716630","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074112740","display_name":"Xiaojing Zhong","orcid":"https://orcid.org/0000-0002-7467-031X"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaojing Zhong","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China"],"raw_orcid":"https://orcid.org/0000-0002-7467-031X","affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101232948","display_name":"Chaolong Luo","orcid":"https://orcid.org/0009-0009-6074-5665"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chaolong Luo","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022852987","display_name":"Xiaowu Dong","orcid":"https://orcid.org/0000-0002-2178-4372"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaowu Dong","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065413047","display_name":"Dingyong Bai","orcid":"https://orcid.org/0000-0002-3839-8013"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dingyong Bai","raw_affiliation_strings":["School of Mathematics, Guangzhou University, Guangzhou 510006, China"],"raw_orcid":"https://orcid.org/0000-0002-3839-8013","affiliations":[{"raw_affiliation_string":"School of Mathematics, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076706292","display_name":"Guiyun Liu","orcid":"https://orcid.org/0000-0002-4830-8878"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guiyun Liu","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China"],"raw_orcid":"https://orcid.org/0000-0002-4830-8878","affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101065140","display_name":"Ying Xie","orcid":"https://orcid.org/0000-0001-6334-3869"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ying Xie","raw_affiliation_strings":["School of Public Administraion, Guangzhou University, Guangzhou 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Public Administraion, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059744858","display_name":"Yuqing Peng","orcid":"https://orcid.org/0009-0005-8066-6914"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuqing Peng","raw_affiliation_strings":["School of Journalism and Communication, Guangzhou University, Guangzhou 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Journalism and Communication, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5059744858","https://openalex.org/A5101065140"],"corresponding_institution_ids":["https://openalex.org/I37987034"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.152,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.89508256,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"25","issue":"8","first_page":"1192","last_page":"1192"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11147","display_name":"Misinformation and Its Impacts","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11147","display_name":"Misinformation and Its Impacts","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9983000159263611,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9969000220298767,"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/rumor","display_name":"Rumor","score":0.9873054027557373},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6152350306510925},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5205863118171692},{"id":"https://openalex.org/keywords/mechanism","display_name":"Mechanism (biology)","score":0.5172932147979736},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.47842007875442505},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4371614456176758},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4245993196964264},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2578083276748657},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14077594876289368},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.14012548327445984}],"concepts":[{"id":"https://openalex.org/C2780469804","wikidata":"https://www.wikidata.org/wiki/Q878352","display_name":"Rumor","level":2,"score":0.9873054027557373},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6152350306510925},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5205863118171692},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.5172932147979736},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.47842007875442505},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4371614456176758},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4245993196964264},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2578083276748657},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14077594876289368},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.14012548327445984},{"id":"https://openalex.org/C39549134","wikidata":"https://www.wikidata.org/wiki/Q133080","display_name":"Public relations","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e25081192","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25081192","pdf_url":"https://www.mdpi.com/1099-4300/25/8/1192/pdf?version=1691716630","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:37628221","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37628221","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:pubmedcentral.nih.gov:10453787","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10453787","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10453787/pdf/entropy-25-01192.pdf","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"},{"id":"pmh:oai:doaj.org/article:874e590677444d858ca01acd176068aa","is_oa":true,"landing_page_url":"https://doaj.org/article/874e590677444d858ca01acd176068aa","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 25, Iss 8, p 1192 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/25/8/1192/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e25081192","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; Volume 25; Issue 8; Pages: 1192","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e25081192","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25081192","pdf_url":"https://www.mdpi.com/1099-4300/25/8/1192/pdf?version=1691716630","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385740893.pdf","grobid_xml":"https://content.openalex.org/works/W4385740893.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1494628843","https://openalex.org/W2050316258","https://openalex.org/W2075941199","https://openalex.org/W2078368246","https://openalex.org/W2145100659","https://openalex.org/W2790166049","https://openalex.org/W2897374016","https://openalex.org/W2913284871","https://openalex.org/W2946154074","https://openalex.org/W2952743423","https://openalex.org/W2955151645","https://openalex.org/W2955396105","https://openalex.org/W2966655750","https://openalex.org/W2989241038","https://openalex.org/W2993575813","https://openalex.org/W3002392201","https://openalex.org/W3013846983","https://openalex.org/W3019863923","https://openalex.org/W3022129833","https://openalex.org/W3028193185","https://openalex.org/W3048952105","https://openalex.org/W3111039657","https://openalex.org/W3114938503","https://openalex.org/W3117477995","https://openalex.org/W3134600612","https://openalex.org/W3215174878","https://openalex.org/W4281558614","https://openalex.org/W4292640189","https://openalex.org/W4294879429","https://openalex.org/W4297330018","https://openalex.org/W6681443325","https://openalex.org/W6755336914","https://openalex.org/W6763286101","https://openalex.org/W6771414595","https://openalex.org/W6787284815","https://openalex.org/W6842067884","https://openalex.org/W6842942270"],"related_works":["https://openalex.org/W2372853429","https://openalex.org/W2793319716","https://openalex.org/W3110636174","https://openalex.org/W4210503589","https://openalex.org/W2810386322","https://openalex.org/W2908713064","https://openalex.org/W2801267666","https://openalex.org/W4213140416","https://openalex.org/W2188429085","https://openalex.org/W2886888575"],"abstract_inverted_index":{"With":[0],"the":[1,27,35,53,60,71,80,91,97,138,145,148],"development":[2],"of":[3,26,37,63,93,99,109,147],"information":[4,12],"technology,":[5],"individuals":[6],"are":[7],"able":[8],"to":[9,58,90,115],"receive":[10],"rumor":[11,49,74,100,117,124],"through":[13,151],"various":[14],"channels":[15],"and":[16,31,83,96,132],"subsequently":[17],"act":[18],"based":[19,126],"on":[20,127],"their":[21,84],"own":[22],"perceptions.":[23],"The":[24,86],"significance":[25],"disparity":[28],"between":[29],"media":[30,94],"individual":[32,56],"cognition":[33,57],"in":[34,55,65],"propagation":[36,50,61,125],"rumors":[38,64],"cannot":[39],"be":[40],"underestimated.":[41],"In":[42],"this":[43],"paper,":[44],"we":[45,69,103,133,142],"establish":[46],"a":[47,107,128],"dual-layer":[48],"model":[51],"considering":[52],"differences":[54],"study":[59],"behavior":[62],"multiple":[66],"channels.":[67],"Firstly,":[68],"obtain":[70],"threshold":[72,87],"for":[73,137],"disappearance":[75],"or":[76],"persistence":[77],"by":[78],"solving":[79],"equilibrium":[81],"points":[82],"stability.":[85],"is":[88],"related":[89],"number":[92,98],"outlets":[95],"debunkers.":[101],"Moreover,":[102],"have":[104,143],"innovatively":[105],"designed":[106],"class":[108],"non-periodic":[110],"intermittent":[111],"noise":[112],"stabilization":[113],"methods":[114],"suppress":[116],"propagation.":[118],"This":[119],"method":[120],"can":[121],"effectively":[122],"control":[123,130,139],"flexible":[129],"scheme,":[131],"provide":[134],"specific":[135],"expressions":[136],"intensity.":[140],"Finally,":[141],"validated":[144],"accuracy":[146],"theoretical":[149],"proofs":[150],"experimental":[152],"simulations.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}
