We present a detailed investigation of the behavior of the nonlinear q-votermodel for opinion dynamics. At the mean-field level we derive analytically, forany value of the number q of agents involved in the elementary update, thephase diagram, the exit probability and the consensus time at the transitionpoint. The mean-field formalism is extended to the case that the interactionpattern is given by generic heterogeneous networks. We finally discuss the caseof random regular networks and compare analytical results with simulations.
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