We study the evolution of the Axelrod model for cultural diversity. We
consider a simple version of the model in which each individual is
characterized by two features, each of which can assume q possibilities. Within
a mean-field description, we find a transition at a critical value q_c between
an active state of diversity and a frozen state. For q just below q_c, the
density of active links between interaction partners is non-monotonic in time
and the asymptotic approach to the steady state is controlled by a time scale
that diverges as (q-q_c)^{-1/2}.Comment: 4 pages, 5 figures, 2-column revtex4 forma

F Vazquez

Gunton J. D.

Klemm K. Eguiluz V. M. Toral R. San Miguel M.

Liggett T. M.

Marro J.

S Redner

Vazquez F.

EPL (Europhysics Letters)

English

arXiv

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 $q < q_{c}$ and a frozen state. For $q\lesssim q_{c}$, 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 $(q-q_{c})^{
-1/2}$

F. Vazquez

S. Redner

EDP Sciences OAI-PMH repository (1.2.0)

Non-monotonicity and divergent time scale in Axelrod  model dynamics

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

Divergent Time Scale in Axelrod Model Dynamics

Abstract

Similar works

Full text

Available Versions

EDP Sciences OAI-PMH repository (1.2.0)

Digital.CSIC

Crossref