Threshold model of language competition including the bilingual state

We propose a threshold model of language competition which includes an intermediate bilingual state. The model is based on the Minett-Wang model but through the introduction of thresholds in the language shift rates, it incorporates the effects of memory and learning. The model is piecewise linear, allowing an exact analytical treatment. We study the symmetric case where two competing languages are equivalent in terms of status and social pressure and provide a complete list of the various dynamical regimes. We also study several limiting regimes corresponding to asymmetric systems and characterize the full spectrum of possible asymptotic behaviors. Unlike the Minett-Wang model, which always predicts the extinction of one of the languages, the proposed model exhibits a wide range of possible equilibrium scenarios, including equilibrium states of coexistence. Most commonly, in such coexistence regimes the minority language speakers are either predominantly monolingual or predominantly bilingual.