{"id":"https://openalex.org/W4383750410","doi":"https://doi.org/10.1109/tac.2022.3200888","title":"Consensus in Concatenated Opinion Dynamics With Stubborn Agents","display_name":"Consensus in Concatenated Opinion Dynamics With Stubborn Agents","publication_year":2023,"publication_date":"2023-07-01","ids":{"openalex":"https://openalex.org/W4383750410","doi":"https://doi.org/10.1109/tac.2022.3200888"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2022.3200888","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3200888","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://liu.diva-portal.org/smash/get/diva2:1790092/FULLTEXT01","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034007972","display_name":"Lingfei Wang","orcid":"https://orcid.org/0000-0001-7046-9478"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lingfei Wang","raw_affiliation_strings":["Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013152161","display_name":"Carmela Bernardo","orcid":"https://orcid.org/0000-0002-6936-2427"},"institutions":[{"id":"https://openalex.org/I16337185","display_name":"University of Sannio","ror":"https://ror.org/04vc81p87","country_code":"IT","type":"education","lineage":["https://openalex.org/I16337185"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carmela Bernardo","raw_affiliation_strings":["Group for Research on Automatic Control Engineering, Department of Engineering, University of Sannio, Benevento, Italy"],"affiliations":[{"raw_affiliation_string":"Group for Research on Automatic Control Engineering, Department of Engineering, University of Sannio, Benevento, Italy","institution_ids":["https://openalex.org/I16337185"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100359415","display_name":"Yiguang Hong","orcid":"https://orcid.org/0000-0001-9505-8739"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiguang Hong","raw_affiliation_strings":["Department of Control Science and Engineering, Tongji University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Control Science and Engineering, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082366820","display_name":"Francesco Vasca","orcid":"https://orcid.org/0000-0002-0960-8683"},"institutions":[{"id":"https://openalex.org/I16337185","display_name":"University of Sannio","ror":"https://ror.org/04vc81p87","country_code":"IT","type":"education","lineage":["https://openalex.org/I16337185"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Vasca","raw_affiliation_strings":["Group for Research on Automatic Control Engineering, Department of Engineering, University of Sannio, Benevento, Italy"],"affiliations":[{"raw_affiliation_string":"Group for Research on Automatic Control Engineering, Department of Engineering, University of Sannio, Benevento, Italy","institution_ids":["https://openalex.org/I16337185"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101779749","display_name":"Guodong Shi","orcid":"https://orcid.org/0000-0002-5929-9655"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I4210127558","display_name":"Australian Centre for Robotic Vision","ror":"https://ror.org/02zv9xv82","country_code":"AU","type":"facility","lineage":["https://openalex.org/I4210127558"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Guodong Shi","raw_affiliation_strings":["Australian Center for Field Robotics, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"Australian Center for Field Robotics, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I4210127558","https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064589174","display_name":"Claudio Altafini","orcid":"https://orcid.org/0000-0003-4142-6502"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Claudio Altafini","raw_affiliation_strings":["Division of Automatic Control, Department of Electrical Engineering, Linköping University, Linköping, Sweden"],"affiliations":[{"raw_affiliation_string":"Division of Automatic Control, Department of Electrical Engineering, Linköping University, Linköping, Sweden","institution_ids":["https://openalex.org/I102134673"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5034007972"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485","https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":4.397,"has_fulltext":true,"cited_by_count":29,"citation_normalized_percentile":{"value":0.94852259,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"68","issue":"7","first_page":"4008","last_page":"4023"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9997000098228455,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9997000098228455,"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/T11804","display_name":"Quantum many-body systems","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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":0.9663000106811523,"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/concatenation","display_name":"Concatenation (mathematics)","score":0.8231434226036072},{"id":"https://openalex.org/keywords/event","display_name":"Event (particle physics)","score":0.641020655632019},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5501884818077087},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4731382429599762},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42810243368148804},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3998681902885437},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3619310259819031},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.35465240478515625},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2274649739265442}],"concepts":[{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.8231434226036072},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.641020655632019},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5501884818077087},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4731382429599762},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42810243368148804},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3998681902885437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3619310259819031},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35465240478515625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2274649739265442},{"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2022.3200888","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3200888","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:DiVA.org:liu-196737","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-196737","pdf_url":"https://liu.diva-portal.org/smash/get/diva2:1790092/FULLTEXT01","source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article in journal"}],"best_oa_location":{"id":"pmh:oai:DiVA.org:liu-196737","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-196737","pdf_url":"https://liu.diva-portal.org/smash/get/diva2:1790092/FULLTEXT01","source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article in journal"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1291590951","display_name":null,"funder_award_id":"2020-03701","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G1783795302","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"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/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/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/G4606321376","display_name":null,"funder_award_id":"2021SHZDZX0100","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5418894820","display_name":null,"funder_award_id":"DP190103615","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5977796052","display_name":null,"funder_award_id":"62173250","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"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/G611870384","display_name":null,"funder_award_id":"grant","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G888693924","display_name":null,"funder_award_id":"DP190103615","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8955107213","display_name":null,"funder_award_id":"Major","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4383750410.pdf","grobid_xml":"https://content.openalex.org/works/W4383750410.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W177913229","https://openalex.org/W1660184077","https://openalex.org/W1976631094","https://openalex.org/W1993380136","https://openalex.org/W1995565680","https://openalex.org/W2019312235","https://openalex.org/W2028706574","https://openalex.org/W2030877649","https://openalex.org/W2046539957","https://openalex.org/W2050592771","https://openalex.org/W2092689551","https://openalex.org/W2099071366","https://openalex.org/W2125668987","https://openalex.org/W2144408773","https://openalex.org/W2145574455","https://openalex.org/W2519326991","https://openalex.org/W2762146562","https://openalex.org/W2898740902","https://openalex.org/W2909528185","https://openalex.org/W2962861899","https://openalex.org/W3099660372","https://openalex.org/W3104269091","https://openalex.org/W3135349069","https://openalex.org/W4200069979","https://openalex.org/W4210681091","https://openalex.org/W4244175652","https://openalex.org/W4244300861"],"related_works":["https://openalex.org/W2373577936","https://openalex.org/W4221148444","https://openalex.org/W4387678054","https://openalex.org/W2389596151","https://openalex.org/W3095575180","https://openalex.org/W4306784355","https://openalex.org/W2169308097","https://openalex.org/W3091984855","https://openalex.org/W2150768546","https://openalex.org/W2570112143"],"abstract_inverted_index":{"This":[0],"article":[1],"investigates":[2],"a":[3,22,27,93,101,109,117],"two-timescale":[4],"opinion":[5],"dynamics":[6],"model,":[7,13],"named":[8],"the":[9,16,19,35,40,43,46,56,69,74,77,87,127,138],"concatenated":[10,94,118],"Friedkin\u2013Johnsen":[11],"(FJ)":[12],"which":[14,116],"describes":[15],"evolution":[17],"of":[18,21,24,29,34,80,86,104,126,142],"opinions":[20,79],"group":[23],"agents":[25,47,57],"over":[26],"sequence":[28],"discussion":[30],"events.":[31],"The":[32],"topology":[33],"underlying":[36],"graph":[37],"changes":[38],"with":[39,60],"event,":[41,54],"in":[42,124],"sense":[44],"that":[45,62,76,92],"can":[48,63,97,121],"participate":[49],"or":[50],"less":[51],"to":[52,68,73],"an":[53,81],"and":[55],"are":[58,113,133],"stubborn,":[59],"stubbornness":[61],"vary":[64],"from":[65],"one":[66],"event":[67,82],"other.":[70],"Concatenation":[71],"refers":[72],"fact":[75],"final":[78],"become":[83],"initial":[84],"conditions":[85,132],"next":[88],"event.":[89],"We":[90],"show":[91],"FJ":[95,119],"model":[96,120],"be":[98],"represented":[99],"as":[100],"time-varying":[102],"product":[103],"stochastic":[105,144],"transition":[106],"matrices":[107],"having":[108],"special":[110,139],"form.":[111],"Conditions":[112],"investigated":[114],"under":[115],"achieve":[122],"consensus":[123],"spite":[125],"stubbornness.":[128],"Four":[129],"different":[130],"sufficient":[131],"obtained,":[134],"mainly":[135],"based":[136],"on":[137],"topological":[140],"structure":[141],"our":[143],"matrices.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}