Concepedia

Global culture: A noise-induced transition in finite systems

Konstantin Klemm, Victor M. Eguı́luz, Raúl Toral, M. San Miguel

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 2003 · 216 citations · 12 references

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TL;DR

The study analyzes how cultural drift, modeled as noise, influences Axelrod’s model of cultural dissemination. The authors examine noise in Axelrod’s model, proving in one dimension that the dynamics can be described by a Lyapunov potential, and in two dimensions that it is governed by the average relaxation time of perturbations. They find that multicultural frozen configurations are unstable, that noise below a critical rate induces monoculture while above it sustains disorder, and that in the thermodynamic limit the relaxation time diverges, allowing global polarization to persist despite local convergence.

Abstract

We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the dissemination of culture. The disordered multicultural frozen configurations are found not to be stable. This general result is proven rigorously in d=1, where the dynamics is described in terms of a Lyapunov potential. In d=2, the dynamics is governed by the average relaxation time T of perturbations. Noise at a rate r <or=T(-1) induces monocultural configurations, whereas r > or =T(-1) sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.