Asymmetric language shift in bilingual communities
Duran, Miquel (supervisors: San Miguel, Maxi and Sánchez, David)
Master Thesis (2023)
Modelling the dynamics of languages in contact is interesting because most of today’s societies are multilingual. It turns out that language coexistence or death are determined by the linguistic prestige and volatility. Thus far, models have focused on equal volatilities for two languages in contact. The aim of this project is to explore a model able to describe a scenario with heterogeneous volatility. In this situation bilinguals are more reluctant to switching to one language than to the other. To that end, this thesis first reviews the Abrams-Strogatz model of language competition, which considers a homogeneous volatility for the whole population, as well as the approach to bilingualism by other models. We then propose a modification to the Abrams-Strogatz model in the mean-field limit to describe the target scenario. The qualitative behaviour of the model is explored and its analytical solutions found and mapped onto a phase space, which is then compared to the results obtained by numerical integration. The main result found is two novel phases, one of extinction of one of the languages and the other with possibility of coexistence, neither found in the Abrams-Strogatz model. Finally, this leads to the discussion about the interpretation of this model, its successes and shortcomings, and how accurately the results obtained could be able to describe real-life scenarios.