{"id":"https://openalex.org/W3135349069","doi":"https://doi.org/10.1109/tac.2021.3052485","title":"Social Power Evolution in Influence Networks With Stubborn Individuals","display_name":"Social Power Evolution in Influence Networks With Stubborn Individuals","publication_year":2021,"publication_date":"2021-02-25","ids":{"openalex":"https://openalex.org/W3135349069","doi":"https://doi.org/10.1109/tac.2021.3052485","mag":"3135349069"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3052485","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3052485","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052680900","display_name":"Ye Tian","orcid":"https://orcid.org/0000-0003-4965-2459"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]},{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["CN","US"],"is_corresponding":true,"raw_author_name":"Ye Tian","raw_affiliation_strings":["Center for Complex Systems, School of Mechano-Electronic Engineering, Xidian University, Xi\u2019an, China","Mechanical Engineering Department and the Center of Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Center for Complex Systems, School of Mechano-Electronic Engineering, Xidian University, Xi\u2019an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"Mechanical Engineering Department and the Center of Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102013222","display_name":"Peng Jia","orcid":"https://orcid.org/0000-0001-6272-8628"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peng Jia","raw_affiliation_strings":["Mechanical Engineering Department and the Center of Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Mechanical Engineering Department and the Center of Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033366105","display_name":"Anahita Mirtabatabaei","orcid":"https://orcid.org/0000-0002-7817-1913"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anahita MirTabatabaei","raw_affiliation_strings":["Mechanical Engineering Department and the Center of Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Mechanical Engineering Department and the Center of Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100447536","display_name":"Long Wang","orcid":"https://orcid.org/0000-0001-5600-8157"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Long Wang","raw_affiliation_strings":["Center for Systems and Control, College of Engineering, Peking University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Center for Systems and Control, College of Engineering, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020551548","display_name":"Noah E. Friedkin","orcid":"https://orcid.org/0000-0001-7826-993X"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Noah E. Friedkin","raw_affiliation_strings":["Department of Sociology and the Center for Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Sociology and the Center for Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068353454","display_name":"Francesco Bullo","orcid":"https://orcid.org/0000-0002-4785-2118"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Francesco Bullo","raw_affiliation_strings":["Mechanical Engineering Department and the Center of Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Mechanical Engineering Department and the Center of Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5052680900"],"corresponding_institution_ids":["https://openalex.org/I149594827","https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":4.7333,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.95795767,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"67","issue":"2","first_page":"574","last_page":"588"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":1.0,"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":1.0,"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":0.9945999979972839,"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/T11031","display_name":"Game Theory and Applications","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.674919605255127},{"id":"https://openalex.org/keywords/phenomenon","display_name":"Phenomenon","score":0.6608248353004456},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5542447566986084},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5411232709884644},{"id":"https://openalex.org/keywords/autocracy","display_name":"Autocracy","score":0.46835508942604065},{"id":"https://openalex.org/keywords/democracy","display_name":"Democracy","score":0.445085734128952},{"id":"https://openalex.org/keywords/interpersonal-communication","display_name":"Interpersonal communication","score":0.42295706272125244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41900891065597534},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38385850191116333},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.3492116928100586},{"id":"https://openalex.org/keywords/social-psychology","display_name":"Social psychology","score":0.2845315635204315},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.25120633840560913},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.24237635731697083},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.10822784900665283},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09120479226112366},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.09015196561813354}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.674919605255127},{"id":"https://openalex.org/C50335755","wikidata":"https://www.wikidata.org/wiki/Q483247","display_name":"Phenomenon","level":2,"score":0.6608248353004456},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5542447566986084},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5411232709884644},{"id":"https://openalex.org/C144661447","wikidata":"https://www.wikidata.org/wiki/Q173424","display_name":"Autocracy","level":4,"score":0.46835508942604065},{"id":"https://openalex.org/C555826173","wikidata":"https://www.wikidata.org/wiki/Q7174","display_name":"Democracy","level":3,"score":0.445085734128952},{"id":"https://openalex.org/C164850336","wikidata":"https://www.wikidata.org/wiki/Q3685487","display_name":"Interpersonal communication","level":2,"score":0.42295706272125244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41900891065597534},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38385850191116333},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.3492116928100586},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.2845315635204315},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.25120633840560913},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.24237635731697083},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.10822784900665283},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09120479226112366},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.09015196561813354},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2021.3052485","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3052485","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6800000071525574,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G3029348492","display_name":null,"funder_award_id":"61533001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3181167558","display_name":null,"funder_award_id":"62036002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4852649143","display_name":null,"funder_award_id":"W911NF-15-1-0577","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G5232561889","display_name":null,"funder_award_id":"61751301","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/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"},{"id":"https://openalex.org/F4320338295","display_name":"Army Research Laboratory","ror":"https://ror.org/011hc8f90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W570916743","https://openalex.org/W1020659046","https://openalex.org/W1660184077","https://openalex.org/W1711105144","https://openalex.org/W1967509640","https://openalex.org/W1998692453","https://openalex.org/W2092689551","https://openalex.org/W2104691143","https://openalex.org/W2110538410","https://openalex.org/W2114747139","https://openalex.org/W2134889984","https://openalex.org/W2222283188","https://openalex.org/W2414538002","https://openalex.org/W2519326991","https://openalex.org/W2534090929","https://openalex.org/W2580802338","https://openalex.org/W2607816388","https://openalex.org/W2761626618","https://openalex.org/W2796112166","https://openalex.org/W2900401143","https://openalex.org/W2962861899","https://openalex.org/W2963927614","https://openalex.org/W2983992771","https://openalex.org/W3083024126","https://openalex.org/W3104530023","https://openalex.org/W4234078673","https://openalex.org/W4235485079","https://openalex.org/W4297926604"],"related_works":["https://openalex.org/W4294983171","https://openalex.org/W3092012512","https://openalex.org/W2363416531","https://openalex.org/W2488113975","https://openalex.org/W3036027526","https://openalex.org/W4285415956","https://openalex.org/W1530014516","https://openalex.org/W2796315259","https://openalex.org/W2228857922","https://openalex.org/W2067400826"],"abstract_inverted_index":{"This":[0],"article":[1],"studies":[2],"the":[3,20,25,29,46,52,56,72,87,93,102,132,136],"evolution":[4],"of":[5,60,74,138],"social":[6,96,104,127],"power":[7,105],"in":[8,115],"influence":[9,111],"networks":[10],"with":[11,131],"stubborn":[12,122],"individuals.":[13],"We":[14,67,98],"formulate":[15],"two":[16],"models":[17,30,54,91],"grounded":[18],"on":[19],"Friedkin\u2013Johnsen":[21],"opinion":[22],"dynamics":[23,49],"and":[24,36,62,78,89,112],"reflected":[26],"appraisal":[27],"mechanism;":[28],"are":[31],"defined":[32],"over":[33,37,45],"issue":[34],"sequences":[35],"a":[38,120],"single":[39],"issue,":[40],"respectively.":[41],"The":[42],"key":[43],"advance":[44],"original":[47,133],"DeGroot\u2013Friedkin":[48,134],"is":[50],"that":[51,86,101],"proposed":[53],"include":[55],"empirically":[57],"observed":[58],"phenomenon":[59],"stubbornness":[61,114,139],"are,":[63],"therefore,":[64],"more":[65,121,125],"realistic.":[66],"obtain":[68],"various":[69],"results":[70],"about":[71],"existence":[73],"equilibria,":[75],"their":[76,79],"uniqueness,":[77],"global":[80],"attractivity.":[81],"For":[82],"example,":[83],"we":[84],"show":[85,100],"single-issue":[88],"issue-sequence":[90],"have":[92],"same":[94],"equilibrium":[95,103,126],"power.":[97,128],"also":[99],"depends":[106],"only":[107],"upon":[108],"interpersonal":[109],"accorded":[110],"individuals\u2019":[113],"several":[116],"cases.":[117],"Roughly":[118],"speaking,":[119],"individual":[123],"has":[124],"In":[129],"comparison":[130],"model,":[135],"introduction":[137],"leads":[140],"to":[141],"fundamental":[142],"sociological":[143],"differences:":[144],"Full":[145],"autocracy":[146],"can":[147,153],"never":[148],"be":[149,154],"achieved,":[150],"whereas":[151],"democracy":[152],"achieved":[155],"under":[156],"all":[157],"network":[158],"topologies.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}