Abstract
One approach for analyzing the dynamics of two languages in competition is to fit historical data for the number of speakers of each with a mathematical model in which the parameters are interpreted as the similarity between those languages and their relative status. Within this approach, on the basis of a detailed analysis and extensive calculations, we show the outcomes that can emerge for given values of these parameters. In contrast to previous results, it is possible that in the long term both languages may coexist and survive. This happens only where there is a stable bilingual group, and this is possible only if the competing languages are sufficiently similar, in which case its occurrence is favoured by both similarity and status symmetry.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. A model is proposed for the case of two languages that compete for speakers in a society without social or spatial structures allowing bilingualism, which enters the model by a parameterization of the similitude among languages. Previous work on the subject, which does not account for bilingualism, arrived at situations where only one language was able to survive in the long term. Here, the simpler situation involving bilingual individuals is adopted, attempting to find a minimalist model that correctly accounts for this phenomenon. The stability of the model is analyzed, seeking situations in which the two languages can coexist.
Main results. From analysis of the stability of the model, it is found that the role played by bilingualism enables stable situations in which both competing languages can survive if some conditions (the number of initial speakers, the similitude of the languages and their relative status) are met. The dynamics of Galician and Castilian (spoken in north-west Spain) are closely reproduced by the proposed equations.
Wider implications. The model sets up a starting point for modeling situations involving bilingualism. Further research incorporating social- or spatial-based interactions should recover this model with a mean-field approach. The model also offers an easy technique for measuring the similitude of two languages which coexist within a certain community.
Figure. Phase space showing the five different behaviors that can take place in this model, depending on the values of status (s) and interlinguistic similarity (k). The regions with the same color indicate that these values (k, s) lead to a similar behavior of the system when introduced in the model. The white spot localizes the parameters k and s of the system Galician–Castilian. The more salient aspect of this map is that the stable existence of a bilingual group requires that k exceed a minimum value of approximately 0.35.