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

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.

30 pages, 11 figures

References in corpus (13)

• Statistical physics of social dynamics
• Analytical Solution of the Voter Model on Disordered Networks
• Ordering dynamics with two non-excluding options: Bilingualism in language competition
• Decelerating microdynamics can accelerate macrodynamics in the voter model
• Langevin description of critical phenomena with two symmetric absorbing states
• Influence of geography on language competition
• Microscopic Abrams-Strogatz model of language competition
• Heterogeneous pair approximation for voter models on networks
• Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior
• Effective surface-tension in the noise-reduced voter model
• Anomalous lifetime distributions and topological traps in ordering dynamics
• Broad lifetime distributions for ordering dynamics in complex networks
• Algebraic coarsening in voter models with intermediate states

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