We investigate the dynamics of two agent based models of language
competition. In the first model, each individual can be in one of two possible
states, either using language X or language Y, while the second model
incorporates a third state XY, representing individuals that use both languages
(bilinguals). We analyze the models on complex networks and two-dimensional
square lattices by analytical and numerical methods, and show that they exhibit
a transition from one-language dominance to language coexistence. We find that
the coexistence of languages is more difficult to maintain in the Bilinguals
model, where the presence of bilinguals in use facilitates the ultimate
dominance of one of the two languages. A stability analysis reveals that the
coexistence is more unlikely to happen in poorly-connected than in fully
connected networks, and that the dominance of only one language is enhanced as
the connectivity decreases. This dominance effect is even stronger in a
two-dimensional space, where domain coarsening tends to drive the system
towards language consensus.Comment: 30 pages, 11 figure