Analytic solution of a model of language competition with bilingualism and interlinguistic similarity

TL;DR

This paper provides a comprehensive analytical study of a language competition model incorporating bilingualism and interlinguistic similarity, clarifying conditions for language coexistence or extinction and refining previous numerical results.

Contribution

It offers the first thorough analytical solution of the model, identifying equilibrium points and phase space, and enhances understanding of language dynamics with potential for model improvements.

Findings

Coexistence of languages depends on model parameters.

Analytical solutions clarify conditions for language extinction.

Phase space analysis reveals possible language evolution trajectories.

Abstract

An in-depth analytic study of a model of language dynamics is presented: a model which tackles the problem of the coexistence of two languages within a closed community of speakers taking into account bilingualism and incorporating a parameter to measure the distance between languages. After previous numerical simulations, the model yielded that coexistence might lead to survival of both languages within monolingual speakers along with a bilingual community or to extinction of the weakest tongue depending on different parameters. In this paper, such study is closed with thorough analytical calculations to settle the results in a robust way and previous results are refined with some modifications. From the present analysis it is possible to almost completely assay the number and nature of the equilibrium points of the model, which depend on its parameters, as well as to build a phase space based on them. Also, we obtain conclusions on the way the languages evolve with time. Our rigorous considerations also suggest ways to further improve the model and facilitate the comparison of its consequences with those from other approaches or with real data.