In Axelrod's model of social influence, the agents are fixed on the sites of a square lattice with connections between nearest neighbors only, and are represented by lists of F features (religious beliefs, education level, social status, etc.) with each feature taking on a number q of distinct values. Following Axelrod, we use the term culture to denote this list of features that is susceptible to changes due to social influence. The interaction between neighboring agents depends on their cultural similarity (homophily) and results in an increase of this similarity (social influence). Depending on the values of the parameters q and F, the steady state of the dynamics may or may not exhibit cultural coexistence and these two outcomes are separated by a non-equilibrium phase transition in the space of parameters of the model. Our main goal is to investigate the classic process of diffusion of innovations using variants of Axelrod's model that include external fields (global media) and a distinctive agent with a fixed cultural feature (the innovation). In this line, we will also study the effect of demographic expansion, i.e., not only the ideas spread from agent to agent, but agents can also move around the lattice.
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