Abstract
We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the exit probability and the consensus time at the transition point. The mean-field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks. We finally discuss the case of random regular networks and compare analytical results with simulations.
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Acknowledgements
R.P.-S. acknowledges financial support from the Spanish MEC, under project No. FIS2010-21781-C02-01; the Junta de Andalucía, under project No. P09-FQM4682; ICREA Academia, funded by the Generalitat de Catalunya; partial support by the NSF under Grant No. PHY1066293, and the hospitality of the Aspen Center for Physics, CO, USA, where part of this work was performed. P.M. acknowledges financial support from Junta de Andalucía project P09-FQM4682 and MICINN–FEDER project FIS2009-08451. S.Y.L. acknowledges the support of the 973 Program of China (No. 2012CB720500) and the National High Technology R&D Program of China (2012AA041102).
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Moretti, P., Liu, S., Castellano, C. et al. Mean-Field Analysis of the q-Voter Model on Networks. J Stat Phys 151, 113–130 (2013). https://doi.org/10.1007/s10955-013-0704-1
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DOI: https://doi.org/10.1007/s10955-013-0704-1