Culture-area relation in Axelrod`s model for culture dissemination

Axelrod`s model for culture dissemination offers a nontrivial answer to the question of why there is cultural diversity given that people`s beliefs have a tendency to become more similar to each other`s as they interact repeatedly. The answer depends on the two control parameters of the model, namely, the number F of cultural features that characterize each agent, and the number q of traits that each feature can take on, as well as on the size A of the territory or, equivalently, on the number of interacting agents. Here, we investigate the dependence of the number C of distinct coexisting cultures on the area A in Axelrod`s model, the culture-area relationship, through extensive Monte Carlo simulations. We find a non-monotonous culture-area relation, for which the number of cultures decreases when the area grows beyond a certain size, provided that q is smaller than a threshold value q (c) = q (c) (F) and F a parts per thousand yen 3. In the limit of infinite area, this threshold value signals the onset of a discontinuous transition between a globalized regime marked by a uniform culture (C = 1), and a completely polarized regime where all C = q (F) possible cultures coexist. Otherwise, the culture-area relation exhibits the typical behavior of the species-area relation, i.e., a monotonically increasing curve the slope of which is steep at first and steadily levels off at some maximum diversity value.

The mass media destabilizes the cultural homogenous regime in Axelrod`s model

An important feature of Axelrod`s model for culture dissemination or social influence is the emergence of many multicultural absorbing states, despite the fact that the local rules that specify the agents interactions are explicitly designed to decrease the cultural differences between agents. Here we re-examine the problem of introducing an external, global interaction-the mass media-in the rules of Axelrod`s model: in addition to their nearest neighbors, each agent has a certain probability p to interact with a virtual neighbor whose cultural features are fixed from the outset. Most surprisingly, this apparently homogenizing effect actually increases the cultural diversity of the population. We show that, contrary to previous claims in the literature, even a vanishingly small value of p is sufficient to destabilize the homogeneous regime for very large lattice sizes.

Effect of external fields in Axelrod's model of social dynamics

The study of the effects of spatially uniform fields on the steady-state properties of Axelrod's model has yielded plenty of counterintuitive results. Here, we reexamine the impact of this type of field for a selection of parameters such that the field-free steady state of the model is heterogeneous or multicultural. Analyses of both one- and two-dimensional versions of Axelrod's model indicate that the steady state remains heterogeneous regardless of the value of the field strength. Turning on the field leads to a discontinuous decrease on the number of cultural domains, which we argue is due to the instability of zero-field heterogeneous absorbing configurations. We find, however, that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforce homogenization. Although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model, we argue that the dimensionality has a significant impact on the stability of the field-free homogeneous steady state.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.