Effects of the underlying topology on perturbation spreading in the Axelrod model for cultural dissemination

We study the effects of the underlying topologies on a single feature perturbation imposed to the Axelrod model of consensus formation. From the numerical simulations we show that there are successive updates which are similar to avalanches in many self-organized criticality systems when a perturbation is imposed. We find that the distribution of avalanche size satisfies the finite-size scaling (FSS) ansatz on two-dimensional lattices and random networks. However, on scale-free networks with the degree exponent γ ≤ 3 we show that the avalanche size distribution does not satisfy the FSS ansatz. The results indicate that the disordered configurations on two-dimensional lattices or on random networks are still stable against the perturbation in the limit N (network size) → ∞ . However, on scale-free networks with γ ≤ 3 the perturbation always drives the disordered phase into an ordered phase. The possible relationship between the properties of phase transition of the Axelrod model and the avalanche distribution is also discussed.