Dynamics of the competition between two languages
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Dynamics of the competition between two languages A. E. Tchahou Tchendjeu1,2,3 · S. Bowong4,5,6,7 · R. Tchitnga2,3,8 · H. B. Fotsin2 Received: 29 July 2019 / Accepted: 14 May 2020 © Sociedad Española de Matemática Aplicada 2020
Abstract This paper reports a new kind of mathematical model for language competition dynamics using compartmental epidemiological modeling approach. The model describes the competition between two languages, say the predominant one called language 1, and the less spoken language 2, both in the same community. We distinguish three groups of population building the concerned community: one majority speaking language 1, one minority speaking language 2 and a last minority speaking neither language 1 nor language 2. The study of the proposed model includes an analysis of the evolution of the number of speakers over time. This model predicts that language 2 can inevitably disappear if the threshold parameter R0 is less than one. We show that our model is well-posed mathematically and linguistically. We also show that the model has basically two linguistic equilibrium points. A monolingual equilibrium point that corresponds to the case where only one language is spoken: some individuals speak only the language 1 and some others do speak neither language 1, nor language 2. A bilingual equilibrium point which corresponds to the case where all the languages are spoken: some individuals speak both languages 1 and 2, some others speak only language 1, while a third group does speak only language 2, and the last group speaks none of the two languages. In this bilingual equilibrium point, both languages coexist. Depending on the threshold parameter, we demonstrate the stability of these equilibria. The model presents on one hand, a direct bifurcation phenomenon, in which we have a stable equilibrium point without bilingual speakers when the associated basic reproduction number is less than one. On the other hand, it presents a stable bilingual equilibrium point when the number of associated basic reproductions is greater than one. The analysis of the overall sensitivity of the model is performed and the impact of the system parameters on the basic reproduction number was performed using sensitivity analysis to determine the impact of each parameter of the system on bilingualism. The numerical simulations carried out are in agreement with the presented theory Keywords Language competition · Bilingualism · Compartmental modeling · Dynamical system · Stability Mathematics Subject Classification 92B05 · 34A30
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1 Introduction In the world, a good number of languages are shrinking with hard evidence. According to the studies on language contact recently done by [3], around 50% of the 6000 languages spoken today are critically endangered and facing disappearance. In many countries, national languages are in competition with official languages. Most of the time, this competition endangers national languages.
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