Modeling language competition in a bilingual community

Abstract

The purpose of this study — construction and research of a new mathematical model of a bilingual community, which takes into account: the effect of mutual assistance within a group of speakers of the same language, the effect of language acquisition by children of bilingual parents at an early age, different prestige of languages for adults. Methods. A new model is being built that takes into account new effects. The model is studied using classical methods with an unlimited increase in dynamics time. The effect of mutual assistance is compared with the effect of language volatility introduced by Abrams and Strogatti. Based on the observed statistical data, using the regression method, the parameters of some languages of England and Canada are determined: Welsh, Scottish, English, French. A forecast is being made for the further development of dynamics. Results. The effects taken into account in the model are confirmed by the correspondence of the development of language dynamics to the characteristics of the language: large values of the parameters of mutual assistance correspond to such a development of language dynamics in which one language displaces the second; at low values of mutual assistance, languages coexist. To model language dynamics using the new model, real statistical data on language pairs is used: Welsh-English, Scots-English, French-English. A forecast is being made for the further development of dynamics by language. Conclusion. General concepts in language dynamics have been supplemented with new ones — the power of mutual assistance within a group of speakers of the same language. The similarity between the effect of language volatility and the effect of mutual assistance is noted.

Keywords

• extinction of languages
• mutual aid effect
• language volatility
• bilingualism
• language competition
• language dynamics
• language preservation
• mathematical model
• ordinary differential equations