Competitiveness Function for a Bilingual Community Model
Abstract
The purpose of this work is to construct competitiveness functions for the bilingual community model.
Materials and methods. The work uses a new model of a bilingual community, which takes into account: the effect of acquiring a second language at an early age; the effect of mutual assistance within a group of the same language. In the model, languages are characterized by parameters of prestige, the likelihood of language acquisition at an early age, the parameter of mutual assistance and the initial number of native speakers. The problem of determining the results of language competition based on their characteristic parameters is considered.
Results. A new method for solving the problem of the results of language competition is proposed. For this purpose, a new concept is introduced in linguistic dynamics: the competitiveness function. To restore the competitiveness function, a ranking method is used, which is related to dividing ordered pairs of languages (under fixed initial conditions) into two classes “the first language displaces the second” and “the second language displaces the first”. The competitiveness function is sought in the form of a power function depending on the language parameters. In this case, the values of the function coefficients are identified based on the processing of available data on the dynamics of the model. The values of the competitiveness functions are analyzed, the results are compared with the observed statistics, and on this basis a forecast is made for the further development of dynamics. The application of this technique is demonstrated on a model in which finding a solution in analytical form is difficult.
Conclusion. The proposed methodology for constructing the competitiveness function is quite general and can be applied to a wide range of models describing population dynamics. The forecast made on the basis of the constructed competitiveness functions agrees well with empirical data.
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