Dietrich Stauffer, Adriano Sousa and Christian Schulze (2004)
Discretized Opinion Dynamics of The Deffuant Model on Scale-Free Networks
Journal of Artificial Societies and Social Simulation
vol. 7, no. 3
<https://www.jasss.org/7/3/7.html>
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Received: 23-Oct-2003 Accepted: 23-Mar-2004 Published: 30-Jun-2004
Figure 1. Number of different surviving opinions versus total number Q of opinions, for various network sizes N. Data for N = 10 and N = 10^{5} are connected by lines. |
Figure 2. Scaled plot of the same data as in Fig.1. The straight lines indicate the ”trivial” scaling limit: Everybody keeps its own opinion in the right part, and each opinion is shared by many in the left part. |
Figure 3. Evidence that cluster numbers for fixed N/Q (here taken as 100) are extensive, for large systems up to 10 million nodes, with N and Q increasing from bottom to top. For small systems the results (line) are very different. All data are summed over 1000 runs. |
Figure 4. As Fig.1, but with noise, for N = 10 (curve) to 10000. The straight line gives S = Q. For smaller Q at N > 100, no convergence within 10^{6} iterations was found. |
Figure 5. As Fig.1, no noise, for Q = 1000 as a function of the length L = Qd of the confidence interval, for N = 10, 100, 1000 (from bottom to top). The larger N is the more pronounced is the transition to complete consensus at L = 500 or d = 1/2. |
(a) | |
(b) | |
(c) | |
Figure 6. Triad formation: a) Log-log plot: Clustering coefficient versus the network size N at probability p_{tf} = 0.00, 0.15, 0.30, 0.45, 0.60, 0.75. 0.90 (from bottom to top) to perform a triad formation step. b) Linear plot: Clustering coefficient versus the probability p_{tf} to perform a triad formation step at N = 10^{4}. c) Log-log plot: Number of different surviving opinions versus total number Q of opinions, for various network sizes N on a scale-free network with triad formation step. The triad formation probability is p_{tf} = 0.3 |
Figure 7. Size distribution for the clusters of different surviving opinions, summed over 100 samples, for network sizes N = 1000...50, 000 on the directed a scale-free network with continuous opinions as in the standard model (Deffuant 2000; Deffuant 2002; Weisbuch 2002). |
Figure 8. Multilayer model: Number of different surviving opinions versus confidence interval L for Q = 10 possible opinions. (For Q = 100 instead of 10 we plot the number versus L/10 instead of versus L, also in Figures 9 and 10.) We see complete consensus for L/Q > 0.6. Part (a) stops the simulation if in the whole system no one changed opinion during one iteration, while in part b we stopped it if the baby layer did not change over ten consecutive iterations. |
Figure 9. Number of different surviving opinions versus L in multilayer model in case of advertising. For a monolayer this number increases up to nearly 8. |
Figure 10. Fraction of advertising successes in multilayer model. For a monolayer the results for L/Q > 0.4 are similar but for L/Q = 0.1 the success fraction is at most 0.1. And for Q = 100 the monolayer success ratio was even lower. |
parameter(nsites=10 ,m=3,iseed=4711,maxt=1000000,iq=1000
1 ,nrun=1000,max=nsites+m, length=1+2*m*nsites+m*m) integer*8 ibm,mult dimension list(length),neighb(max,m),is(max),nhist(0:iq), 1 number(max), ns(31),irand(0:3) data irand/0,0,-1,1/ w=sqrt(0.1) print 100, iq, nsites, m, iseed, maxt, nrun, w 100 format('# directed, more confidence', 6i9,f6.3) factor=(0.25d0/2147483648.0d0)/2147483648.0d0 facto2=factor*2*iq mult=13**7 mult=mult*13**6 ibm=2*iseed-1 do 35 idis=100,900,100 derrisum=0.0 do 16 i=1,31 16 ns(i)=0 ict=0 do 17 irun=1,nrun do 29 n=1,max 29 number(n)=0 do 7 i=1,m do 7 nn=1,m neighb(i,nn)=nn 7 list((i-1)*m+nn)=nn L=m*m c All m initial sites are connected with each other and themselves do 1 i=m+1,max do 2 new=1,m 4 ibm=ibm*16807 j=1+(ibm*factor+0.5)*L if(j.le.0.or.j.gt.L) goto 4 j=list(j) list(L+new)=j list(L+m+new)=i 2 neighb(i,new)=j 1 L=L+2*m c end of network and neighbourhood construction, start of opinion change n=max do 5 i=1,n ibm=ibm*16807 5 is(i)=1+iabs(ibm)*facto2 c print *, is do 9 iter=1,maxt ichange=0 do 10 j=1,n 6 ibm=ibm*16807 i=1+(ibm*factor+0.5)*m if(i.le.0.or.i.gt.m) goto 6 i=neighb(j,i) if(is(i).eq.is(j) .or. iabs(is(i)-is(j)).gt.idis) goto 12 ichange=ichange+1 if(iabs(is(i)-is(j)).eq.1) then ibm=ibm*16807 if(ibm.lt.0) then is(i)=is(j) else is(j)=is(i) end if else idiff=isign(ifix(0.5+w*iabs((is(i)-is(j)))),is(i)-is(j)) is(j)=is(j)+idiff is(i)=is(i)-idiff endif c10 print *, iter, is(j) 12 continue c ibm=ibm*mult c index=ishft(ibm,-62) c noise c is(j)=min0(iq,max0(irand(index)+is(j),1)) 10 continue c if(iter.eq.(iter/1000 )*1000 ) print *, iter,ichange if(ichange.eq.0) goto 11 9 continue print *, 'not converged' 11 continue do 28 i=0,iq 28 nhist(i)=0 do 25 i=1,n j=is(i) 25 nhist(j)=nhist(j)+1 c print *, iter, nhist icount=0 do 27 i=1,iq if(nhist(i).gt.0) icount=icount+1 if(icount.gt.0) number(icount)=number(icount)+nhist(i) 27 continue ict=ict+icount c print *, irun,icount,iter icount=0 do 33 i=1,max 33 icount=icount+number(i) derrida=0.0 fact=1.0/icount**2 do 34 i=1,max 34 derrida=derrida+fact*number(i)**2 do 31 i=1,max if(number(i).eq.0) goto 31 ibin=1+alog(float(number(i)))/0.69315 ns(ibin)=ns(ibin)+1 31 continue c print *, irun,icount,iter,iq,derrida derrisum=derrisum+derrida 17 continue derrida=derrisum/nrun c do 32 i=1,31 c32 if(ns(i).gt.0) print *, 2**(i-1), ns(i) call flush(6) 35 print *, idis, ict*1.0/nrun, derrida stop end |
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