A nonlinear q-voter model with deadlocks on the Watts–Strogatz graph

Abstract

.We study the nonlinear q-voter model with deadlocks on a Watts–Strogatz graph characterized by two parameters k and β. Using Monte Carlo simulations, we obtain a so-called exit probability and an exit time. We determine how network properties, such as randomness or density of links, influence the exit properties of a model. In particular we show that the exit probability, which is the probability that the system ends up with all spins up, starting with the p fraction of up-spins, has the general form E(p) = pα/(pα + (1 − p)α). Moreover, using the finite-size scaling technique we show that the exit probability exponent α depends both on the parameter q as well as the network structure, i.e. k and β.