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A reaction–diffusion model for competing languages

  • New Trends in Fluid and Solid Mechanical Models
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Abstract

The extinction of many of the world’s minority languages is of great concern as language death can lead to the irrevocable loss of cultural information. This often occurs through a process of language shift, where individuals switch from speaking one language to a different, more dominant, language. To prevent the loss of language, it is necessary to determine whether language loss is inevitable or if languages can coexist. We address this question by constructing a nonlinear system of reaction–diffusion equations to model the spread of two competing languages, u and v, which vary temporally and spatially. Language u is assumed to confer a relative status advantage to its speakers, thus individuals may convert from language v to language u. The four constant system equilibria are found. Instability and stability conditions are found for each equilibrium. We conclude that the coexistence of both languages u and v is globally stable, subject to certain constraints on the growth rate of each language and the initial values of both u and v.

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Acknowledgments

I would like to thank Jeremy R. Kendal and Brian Straughan for helpful conversations.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK

    Caroline E. Walters

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  1. Caroline E. Walters
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Correspondence to Caroline E. Walters.

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Walters, C.E. A reaction–diffusion model for competing languages. Meccanica 49, 2189–2206 (2014). https://doi.org/10.1007/s11012-014-9973-2

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  • DOI: https://doi.org/10.1007/s11012-014-9973-2

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