Threshold model of language competition including the bilingual state

Area of Science:

• Sociolinguistics
• Mathematical Modeling
• Dynamical Systems

Background:

• Language competition models often predict the extinction of one language.
• Existing models may not fully capture the nuances of bilingualism and learning.
• The Minett-Wang model is a foundational framework for studying language dynamics.

Purpose of the Study:

• To propose a novel threshold model for language competition that includes an intermediate bilingual state.
• To incorporate the effects of memory and learning into language shift dynamics.
• To explore a wider range of equilibrium scenarios beyond language extinction.

Main Methods:

• Development of a piecewise linear threshold model based on the Minett-Wang model.
• Introduction of thresholds in language shift rates to account for memory and learning.
• Analytical treatment of the symmetric case and study of limiting asymmetric regimes.

Main Results:

• The proposed model allows for exact analytical treatment due to its piecewise linear nature.
• Unlike the Minett-Wang model, this model predicts various equilibrium states, including language coexistence.
• In coexistence scenarios, minority language speakers are often predominantly monolingual or bilingual.

Conclusions:

• The threshold model provides a more realistic representation of language competition by including bilingualism and learning.
• The model's flexibility allows for the prediction of diverse long-term language dynamics, including stable coexistence.
• This framework offers new insights into the factors influencing language vitality and shift.