Threshold model of language competition including the bilingual state

TL;DR

This paper introduces a threshold-based language competition model that includes bilingual states, allowing for diverse outcomes such as language coexistence, unlike previous models that predicted language extinction.

Contribution

It extends the Minett-Wang model by incorporating thresholds and bilingual states, enabling analytical treatment and a broader range of equilibrium scenarios.

Findings

Model predicts coexistence of languages under certain conditions

Bilingual states can be stable equilibria

Diverse asymptotic behaviors identified

Abstract

We propose a threshold model of language competition which includes 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 the 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 new 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 completely monolingual or completely bilingual.