We study the evolution of the Axelrod model for cultural diversity, a prototypical non-equilibrium process that exhibits rich dynamics and a dynamic phase transition between diversity and an inactive state. We consider a simple version of the model in which each individual possesses two features that can assume q possibilities. Within a mean-field description in which each individual has just a few interaction partners, we find a phase transition at a critical value qc between an active, diverse state for q < qc and a frozen state. For q qc, the density of active links is non-monotonic in time and the asymptotic approach to the steady state is controlled by a time scale that diverges as (q−qc)−1/2.

Texto completo preprint.-- 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 89.65.-s Social and economic systems 02.50.Ey Stochastic processes

We thank A. Vespignani for helpful comments on the manuscript and gratefully acknowledge financial support from the US National Science Foundation grant DMR0535503.

Peer reviewed