Diffusion of innovations in Axelrod’s model on small-world networks

The interest in learning how innovations spread in our society has led to the development of a variety of theoretical-computational models to describe the mechanisms that govern the diffusion of new ideas among people. In this paper, the diffusion of innovations is addressed with the use of the Axelrod’s cultural model where an agent is represented by a cultural vector of F features, in which each feature can take on Q integer states. The innovation or new idea is introduced in the population by setting a single feature of a single agent to a new state (Q+1) in the initial configuration. Particularly, we focus on the effect of the small-world topology on the dynamics of the innovation adoption. Our results indicate that the innovation spreads sublinearly (∼t1∕2) in a regular one-dimensional lattice of connectivity K=4, whereas the innovation spreads linearly (∼t) when a nonvanishing fraction of the short-ranged links are replaced by long-range ones. In addition, we find that the small-world topology prevents the emergence of complete order in the thermodynamic limit. For systems of finite size, however, the introduction of long range links causes the dynamics to reach a final ordered state much more rapidly than for the regular lattice.