Agent Based Models of Language Competition: Macroscopic descriptions and Order-Disorder transitions

TL;DR

This paper studies agent-based models of language competition, revealing how network structure and bilingualism influence the transition between language coexistence and dominance, with implications for understanding language dynamics.

Contribution

It introduces and analyzes two models of language competition, highlighting the impact of network connectivity and bilingualism on language coexistence and dominance.

Findings

Coexistence is harder to maintain with bilingual agents.

Lower connectivity favors language dominance.

Two-dimensional spaces promote language consensus.

Abstract

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.