Geodesic
Modeling language competition in a bilingual community
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 32 (2024) no. 5, pp. 691-708.

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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 
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A. V. Medvedev; O. A. Kuzenkov. Modeling language competition in a bilingual community. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 32 (2024) no. 5, pp. 691-708. http://geodesic.mathdoc.fr/item/IVP_2024_32_5_a8/

[1] Abrams D., Strogatz S., “Modelling the Dynamics of Language Death”, Nature, 424 (2003), 900 | DOI

[2] Mira J., Paredes B., “Interlinguistic Similarity and Language Death Dynamics”, Europhysics Letters, 69:6 (2005), 1031–1034 | DOI

[3] Castelly X., Eguiluz V., San Miguel M., “Ordering dynamics with Two non-excluding option: Bilingualism in language competition”, New Journal of Physics, 8:12 (2006), 308 | DOI

[4] Baggs I., Freedman H., “A mathematical model for the dynamics of interactions between a unilingual and a bilingual population: persistence versus extinction”, Journal of Mathematical Sociology, 16:1 (1990), 51–75 | DOI | MR | Zbl

[5] Baggs I., Freedman H., “Can the speakers of a dominated language survive as unilinguals?: A mathematical model of bilingualism”, Mathematical and Computer Modelling, 18:6 (1993), 9–18 | DOI | MR | Zbl

[6] Wyburn J., Hayward J., “The future of bilingualism: an application of the Baggs and Freedman model”, Journal of Mathematical Sociology, 32:4 (2008), 267–284 | DOI | Zbl

[7] Diaz M., Switkes J., “Speaking out: A mathematical model of language preservation”, Heliyon, 7:5 (2021), 2405–2425 | DOI

[8] Aleksandrova N. Sh., “Ischeznovenie yazykov i estestvennyi bilingvizm”, Polilingvialnost i transkulturnye praktiki, 20:3 (2023), 436–455 | DOI

[9] Paradis M., A Neurolinguistic Theory of Bilingualism, John Benjamins Publishing Company, Amsterdam, Philadelphia, 2004, 299 pp. | DOI

[10] Aleksandrova N. Sh., “Rodnoi yazyk, inostrannyi yazyk i yazykovye fenomeny, u kotorykh net nazvaniya”, Voprosy yazykoznaniya, 2006, no. 3, 88–100

[11] Alexandrova N. S., Antonets V. A., Kuzenkov O. A., Nuidel I. V., Shemagina O. V., Yakhno V. G., “Bilingualism as an Unstable State”, Advances in Cognitive Research, Artificial Intelligence and Neuroinformatics. Advances in Intelligent Systems and Computing, 1358 (2021), 359–367 | DOI

[12] Medvedev A. V., Kuzenkov O. A., “Modelirovanie konkurentsii yazykov”, Sovremennye informatsionnye tekhnologii i IT-obrazovanie, 19:2 (2023), 381–392 | DOI

[13] Volterra V., Matematicheskaya teoriya borby za suschestvovanie, Nauka, M., 1976, 286 pp. | MR

[14] Kuzenkov O. A., Ryabova E. A., Matematicheskoe modelirovanie protsessov otbora, Izd-vo Nizhegorodskogo gosuniversiteta, Nizhnii Novgorod, 2007, 323 pp.

[15] Sutantawibul C., Xiao P., Richie S., Fuentes-Rivero D., “Revisit language modeling competition and extinction: A Data-Driven Validation”, Journal of Applied Mathematics and Physics, 6:7 (2018), 1558–1570 | DOI

[16] Menghan Z., Tao G., “Principles of parametric estimation in modeling language competition”, Proceedings of the National Academy of Sciences (PNAS), 110:24 (2013), 194–212 | DOI

[17] Statistics of Canada , Last accessed 3 Sep 2023 https://www.statcan.gc.ca