Non-monotonicity and divergent time scale in Axelrod model dynamicsF. Vazquez and S. Redner
Center for BioDynamics, Center for Polymer Studies, and Department of Physics, Boston University - Boston, MA, 02215, USA
received 1 September 2006; accepted in final form 17 February 2007; published April 2007
published online 19 March 2007
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 , 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.
89.65.-s - Social and economic systems.
02.50.Ey - Stochastic processes.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
© Europhysics Letters Association 2007