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Our earlier language model is modified to allow for the survival of a minority language without higher status, just because of the pride of its speakers in their linguistic identity. An appendix studies the roughness of the interface for linguistic regions when one language conquers the whole territory.
During the last decade, much attention has been paid to language competition in the complex systems community, that is, how the fractions of speakers of several competing languages evolve in time. In this paper, we review recent advances in this direction and focus on three aspects. First, we consider the shift from two-state models to three-state models that include the possibility of bilingual individuals. The understanding of the role played by bilingualism is essential in sociolinguistics. In particular, the question addressed is whether bilingualism facilitates the coexistence of languages. Second, we will analyze the effect of social interaction networks and physical barriers. Finally, we will show how to analyze the issue of bilingualism from a game theoretical perspective.
We study the role played by bilinguals in the competition between two languages and in the formation of a bilingual community. To this aim we introduce a simple three-state model that combines the Minett–Wang model, in which the bilinguals do not affect directly the probability of transition of an individual from monolingualism to bilingualism, and the Baggs–Freedman model, in which such a transition probability only depends on bilinguals. The model predicts the possibility for the existence of a stable bilingual community though no particular conditions are assumed for the two competing languages: the asymptotic stability of the bilinguals community is only due to the type of dynamics regulating the transitions between different linguistic groups. The proposed model and the obtained results give some suggestions for the conditions necessary for the formation of a stable bilingual community. First of all, it is important that the bilinguals are valid representatives of the two languages, in the sense that they are regarded by monolinguals also as speakers of the other language. Besides that, the transition from bilinguals to monolinguals must be smaller than the opposite transition. Unless both these conditions are fulfilled, the stable equilibrium solution of the language competition is a monolingual society.