@article{89350ff1a6e74cd797ba735affbd279c,
title = "On the Analysis of the DeGroot-Friedkin Model with Dynamic Relative Interaction Matrices",
abstract = "This paper analyses the DeGroot-Friedkin model for evolution of the individuals{\textquoteright} social powers in a social network when the network topology varies dynamically (described by dynamic relative interaction matrices). The DeGroot-Friedkin model describes how individual social power (self-appraisal, self-weight) evolves as a network of individuals discuss opinions on a sequence of issues. We seek to study dynamically changing relative interactions because interactions may change depending on the issue being discussed. Specifically, we study relative interaction matrices which vary periodically with respect to the issues. This may reflect a group of individuals, e.g. a government cabinet, that meet regularly to discuss a set of issues sequentially. It is shown that individuals{\textquoteright} social powers admit a periodic solution. Initially, we study a social network which varies periodically between two relative interaction matrices, and then generalise to an arbitrary number of relative interaction matrices.",
keywords = "behavioural sciences, multi-agent systems, networked systems, opinion dynamics, social, social networks",
author = "Mengbin Ye and Ji Liu and Anderson, {Brian D.O.} and Changbin Yu and Tamer Ba{\c s}ar",
note = "Funding Information: gbgorreoociuucappolnsssscooiidffeenpprceeeeoodspp.llfeeSropiifnnefttceeiforriaancccaettlliipynn,ggoianwwtsiiottohhcfiattlhhvieeneiiewrrtwaaaccoqqsruaukaciinnoffttnuaasnnlitsccit-eeiassnggcceaanonntf ofpidtthasetoecpsoinitvisoenxowacnnodfofbtphiinnoaisoetnioonfbiaatssreedndeoiegnthebrafofcuionrnse.dvTebxhyec1oc∆fofetbhfifenicaiietnindotins- bsbyreeostuccepoofnnsf.ssoiiTddf eehprreeeoddepflfferreooriffgnffetenoorcanneceetoifppnsgoooiinnwcttiiatloohffftfhvvediieeeiiwwra apaaclqssauatafoirnffffftfuuasnllttsciiu--eaacsgghceeannanstt vfidtuhael{\textquoteright}csosnevlef-xwceoigfhfbtin(wathioicnh arreepdreesteenrtfsfinseeldf-abpyp1r∆aitshael, isnedlfi-- sFsyyaessctteceeboffnoff..soikTTd,ehhrIeeendseetffaffrgeeorrrfggafeefnnfoccaneeneoodffpTssoooiwnccitiitaatlloefffrffvheeddiaeiiswaaoppnalllsaayttaffioonrrfcfffrffuessaltsssiuue-adccghhtehnaaesst cofidntufhiadele{\textquoteright}csnocsneev∆lef-axwncedoigf2hf∆bttinh(waethwioicenhigahrretespdraeesstseeingrtnfsfeidnseebldfy-abtpyhpe1r∆ainitsdhaielv,iidsneudlafi--l syascteebfof.okT,hIensetfafgerrgaefnf caenodf Tsowciitatlefrfhedaisaopnllaytfionrcfrfesassuedchthaes tooidniuftiasdle{\textquoteright}nsnecisge∆hlfb-awonuedirgs2h∆(twth(hweichwhicehfigfhirgethsptraebsseeingatnsefdfseebalfys-uatprheperoaifnisdtarilvu,isdsteuloafr-l Frealceevbanoocek,oIfnrsetsaegarracfhfoanndsoTciwalitnteetrwhoarskso.nly increased the troineinftisddsenhneicpige∆∆h.baAontudtrhs2e∆(bwthehgeiicnwhneifingfghigtohsftaebsasecihgannefedfwebaiyssusturheee,oaifnrdterifvuleisdcttueoadrl rFelealceeevvbaannoocecek,ofoIfnrrsesearetsaegarraccfhhfonoanndsosoTciciwalalitnnteeettrwwhooarrskks.so.nly increased the froieintsdsnheipig∆h.bAotutrhse(bwehgiicnhnifnfgigohftebaechanfefweaissusuree,oafrterfulesctteodr Arelepvraonbcleefofforfespeaarrtcihcuolnarsoinctiaelrensettwisor“kosp.inion dynaffics”, arpiepnrdaisshailpf∆f.eAchtatnhiesfbfegisinunsiendgboyf eachninedwivisidsuuea,latoreuflpedctaetde Awhpicrhobslteufdfieosf hpoawrtiocpuilnaironinstewrietshtinisa“osopciniailonnedtwynoarkffifcfsa”y, itpsporawinsalseflffe-cwheaignhistf.fTishuissefdfebcyhaenaicshffintdaikveisduianltotoaucpcoduantet Ahpicrhobslteufdfieosf hpoawrtiocpuilnaironinstewrietshtinisa“osopciniailonedtwynoarkffifcfsa”y, itpsporawinsalseflffe-cwheaignhistf.fTishuissefdfebcyhaenaicshffintdaikveisduianltotoaucpcoduantet wevhoilcvhe satusdiinesdihvoidwuaolpsindioisncsuswsitahninisasusoe,ciael.gn.ertweloigrikonffaoyr ithseoinwdnivsiedluf-awl{\textquoteright}esiginhftl.ueTnhciesafnfdecihfafpnaiscftfotnaktehse idnitsocuasscicoonunotf evhoilcvhe satusdiinesdihvoidwuaolpsindioisncsuswsitahninisasusoe,ciael.gn.ertweloigrikonffaoyr tthseoinwdnivsiedluf-awl{\textquoteright}esiginhftl.ueTnhciesafnfdecihfafpnaiscftfotnaktehse idnitsocuasscicoonunotf ★evolve as individuals discuss an issue, e.g. religion or thpeiniinodnisvoidnutahl{\textquoteright}espinrifolureinsscueea.nFdroiffpoancetpoenrstpheectdiivsec,uassnioinndoi-f ★evolve as individuals discuss an issue, e.g. religion or ohpeiniinodnisvoidnutahl{\textquoteright}espinrifolureinsscueea.nFdroiffffpoancetpoenrstpheectdiivsec,uassnioindoi-f (ATfihCis)uwnodrekrtwhaesAsfuiCppgorratnedtsbDyP-t1h3e01A0u36st1r0alaianndDfiPes-e1a6r0c1h04C50o0u,nbciylThisworkwassupportedbytheAustralianfiesearchCouncil vpidinuiaoln{\textquoteright}sssoenlf-twheeigphrtioirsiassrueep.rFersoenfftaotnioenpoefrstpheacttiivned,ivaniduinadl{\textquoteright}is-★ vpidinuiaoln{\textquoteright}sssoenlf-twheeigphrtioirsiassrueep.rFersoenfftaotnioenpoefrstpheacttiivned,ivaniduinadl{\textquoteright}is-(ATfihCis) uwnodrekr twhaesAsfuiCppgorratnedts bDyP-t1h3e01A0u36st1r0alaiannd DfiPes-e1a6r0c1h04C50o0u,nbciyl soidcuiaall{\textquoteright}psosweelfr-wineitghet sisocaiarlepnreetsweonrtka.tion of that individual{\textquoteright}s thefiNCa)tuionndaelrNtahteuArafliCScgiernacnetsFDouPn-d13a0ti1o0n36o1f0CahnindaD(gPr-a1n6t06110347550007,2b)y, soidcuiaall{\textquoteright}psosweelfr-wineitghet sisocaiarlepnreetsweonrtka.tion of that individual{\textquoteright}s thnedNbaytioDnaatlaN61a-tCurSaIlfiSOcie(nfocremFeorulyndNatIiConTAof).ChTihnea(wgorarknto6f13L7iu507a2n)d, social power in the social network. ahnedNbaytioDnaatlaN61a-tCurSaIlfiSOcie(nfocremFeorulyndNatIiConTAof).ChTihnea(wgorarknto6f13L7iu507a2n)d, Tohceialkpeoywecronintrtibhuetsioonciaol fnetthwiosrkp.aper is the study of The key contribution of this paper is the study of BaU¸safirIwGarsanstupNp0o0rt0e1d4-1in6-p1-a2r7t1b0,yaOnfdficienopfarNtabvyalNfiSeFseaurncdher(OgNrafnit) Thhee DkeeGyrocootn-Ftrriibeudtkiionn ffoofdetlhiws itphapisesruei-svartyhiengstiundteyraoc-f thhee DkeeGyrocootn-Ftrriibeudtkiionn ffoofdetlhiws itphapisesruei-svartyhiengstiundteyraoc-f BaU¸safirI wGarsanstupNp0o0rt0e1d4-1in6-p1-a2r7t1b0,y aOnfdficien opfarNtabvyal NfiSeFseaurncdher(OgNrafnit) thoensDaefGforonogt-tFhreieidnkdiinvidffuoadlse.l Bweicthauissesuine-tveararyctiniognsinitnertahce-thoensDaefGforonogt-tFhreieidnkdiinvidffuoadlse.l Bweicthauissesuine-tveararyctiniognsinitnertahce-CCUFfiI11G-1r1a3n4t2.N00014-16-1-2710, and in part by NSF under grant tions affong the individuals. Because interactions in the CCF 11-11342. Copyright {\textcopyright} 2017 IFAC 12408tions affong the individuals. Because interactions in the 2405-8963 {\textcopyright} 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. CPeer review under responsibility of International Federation of Automatic Control.opyright {\textcopyright} 2017 IFAC 12408 Copyright {\textcopyright} 2017 IFAC 12408 10.1016/j.ifacol.2017.08.1426 Publisher Copyright: {\textcopyright} 2017 Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",
year = "2017",
month = jul,
doi = "10.1016/j.ifacol.2017.08.1426",
language = "English (US)",
volume = "50",
pages = "11902--11907",
journal = "IFAC-PapersOnLine",
issn = "2405-8963",
publisher = "IFAC Secretariat",
number = "1",
}