Languages can be viewed as entities competing among each other for speakers, with less advantageous ones eventually dying out. Through such a process, approximately 90% of the worlds languages are predicted to go extinct in the current century [2, 28]. Motivated by this prognosis, the past two decades has seen a surge of interest in the modeling of language competition dynamics, with emphasis being put on systems of two competing languages. The Abrams and Strogatz model (ASM) proposed by in 2001 in Ref. [1] is generally cited as inspiration for the latter. Considering the existence of multi-ethnic regions and the rising effect of globalization (the spread of globally prevalent languages) however, it is also of interest to know the properties of competition between three distinct language groups. We present such a model, as a generalization of the ASM to a three-state variant and find analytical expressions for its stationary points and report their stability criteria, for the case of a power-law type transition function. We present a framework to describe the models dynamics for any initial fractions of speakers and in particular, some interesting phenomenon arising from the interplay of system and language parameters.

In the original version of this article supplied to AIP Publishing, Reference 29 contained an error in the volume number. A revised article, with this item corrected, was published on 17 March 2021.

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