Effects of noise and confidence thresholds in nominal and metric Axelrod dynamics of social influence

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 4, 2009, Pages

  De Sanctis, Luca ^a,b   Galla, Tobias ^b,c  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

^c UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

AXELROD'S MODEL; CONFIDENCE THRESHOLD; DISORDERED STATE; EXTERNAL NOISE; FINITE SYSTEMS; MASTER EQUATIONS; MEAN-FIELD; NOMINAL FEATURE; NUMERICAL SIMULATION; SIMILARITIES AND DIFFERENCES; SOCIAL INFLUENCE; THERMODYNAMIC LIMITS;

EID: 67650460009     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.046108     Document Type: Article

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32. We here do not impose the constraint that R be connected as it is often done in the literature. This simplifies the numerical determination of the size of the largest homogeneous region. Results regarding the phase structure do not depend on whether or not connectedness is assumed in the definition of homogeneous regions. In particular the ordered phase consists of one region spanning the entire system, so that both definitions yield the same characterization of the low- q phase.
33. Integration of the master equation yields a positive value for the fraction of active bonds in the ordered phase (coarsening lasts indefinitely in infinite systems in the ordered phase) and a vanishing fraction in the disordered phase, similar to. The location of the phase transition in Fig. 3 is obtained as the point where the number of active bonds decreases below a threshold on the order of 10-3, or equivalently as the point at which a discontinuity in PF or its derivative occurs.
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35. Rescaling both axes in Fig. 3 and plotting the phase boundaries in (/F,q/F) plane give an equally good collapse.
36. We here note that the data shown in Fig. 6 suggest that PF at stationarity might potentially be a decreasing function of δ for r 0.01. PF is small for all tested values of δ in this regime, however, so that we have not investigated this regime further.
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