In the general context of models of consensus through social interaction, such as the voter model and the kinetic Ising model at T=0 with Glauber dynamics, we study a 3 non-equivalent states agent based model (ABM) proposed by Minett and Wang for the dynamics of language competition. In this work, we restrict our analysis to the case of
socially equivalent languages. In the first place, we study the model in a two dimensional regular lattice, analyzing the effects of locality in the dynamics. Coarsening processes and interface dynamics are analysed, obtaining a power law decay for the average interface density. In the second place, we analyze the dynamics on a small world network to study the effects on the dynamics when moving from a regular lattice to a random network. Finally, we compare the present results with our previous work on the analysis of the ABM of Abrams-Strogatz dynamics, where bilinguals were not taken into account; getting interesting results about the role of bilinguals depending on the social structure.
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