Phase transitions in the q-voter model with noise on a duplex clique

Anna Chmiel and Katarzyna Sznajd-Weron
Phys. Rev. E 92, 052812 – Published 24 November 2015

Abstract

We study a nonlinear q-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. To study the role of the multilevelness in this model we propose three methods of transferring the model from a mono- to a multiplex network. They take into account two criteria: one related to the status of independence (LOCAL vs GLOBAL) and one related to peer pressure (AND vs OR). In order to examine the influence of the presence of more than one level in the social network, we perform simulations on a particularly simple multiplex: a duplex clique, which consists of two fully overlapped complete graphs (cliques). Solving numerically the rate equation and simultaneously conducting Monte Carlo simulations, we provide evidence that even a simple rearrangement into a duplex topology may lead to significant changes in the observed behavior. However, qualitative changes in the phase transitions can be observed for only one of the considered rules: LOCAL&AND. For this rule the phase transition becomes discontinuous for q=5, whereas for a monoplex such behavior is observed for q=6. Interestingly, only this rule admits construction of realistic variants of the model, in line with recent social experiments.

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  • Received 11 March 2015
  • Revised 20 July 2015

DOI:https://doi.org/10.1103/PhysRevE.92.052812

©2015 American Physical Society

Authors & Affiliations

Anna Chmiel and Katarzyna Sznajd-Weron

  • Department of Theoretical Physics, Wroclaw University of Technology, Wroclaw, Poland

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Issue

Vol. 92, Iss. 5 — November 2015

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