Competitiveness Function for the Generalized Abrams-Strogatti Model in the Case of Non-constant Community Size

The purpose of this work is to construct competitiveness function for the modified Abrams-Strogatti model describing the competition of several languages. Materials and methods. The modified model differs from the original Abrams-Strogatti model in that: volatility may be different for each language; the number of competing languages in a community is not limited (unlike the bilingual Abrams-Strogatti community); changes in the size of the community are allowed. Languages are characterized by parameters of prestige, volatility and the initial number of native speakers. The problem of determining the results of language competition by their characteristic parameters is considered. Results. A new method of solving the problem of the results of language competition is proposed. For this purpose, a new concept is introduced in language dynamics: the competitiveness function. To restore the competitiveness function, a ranking method is used. The competitiveness function is sought in the form of a power function depending on the language parameters. The values of the competitiveness function are analyzed, and on its basis a forecast is made for the further development of dynamics. At the first stage, the methodology is tested on a model that has an analytical solution. At the second stage, its application is demonstrated in the case when 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 the dynamics of populations. The forecast made on the basis of the constructed competitiveness functions is in good agreement with empirical data.