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<p>Languages develop through a complex interplay of communal competition, shaped by both social and ecological dynamics. While there are thousands of languages spoken globally, many are at risk of disappearing due to changes in language usage and the dominance of more widely spoken languages. Studying and modeling language preservation is crucial, as language directly effects the cultural identity and heritage it represents. This manuscript presents analysis of linguistics dynamics between a bilingual and monolingual population, employing a mathematical model that uses a system of highly non-linear differential equations. For the solution and analysis of the language model, we have applied He-Laplace Carson algorithm by creating multiple homotopies related to the perturbation method. The solution profiles for both the monolinguals as well as bilinguals has been created, which are put to further scrutiny by investigating graphically in detail the prominent parameters such as mass action interaction parameter, language status parameter and immigration rate parameter etc. involved in our model. Furthermore, to ascertain the accuracy and dependability of our proposed method, we have also presented concise and definite numerical validation in all cases involved by finding out the residual errors. Additionally, the fractional parameter is analyzed under different constraints and conditions, with the results presented visually using 2D and 3D plots, as well as gradient contour diagrams. Building on previous mathematical models, our approach incorporates population proportions within a simple structure, resulting in key patterns such as a stable spiral that allows all three language groups to persist. The conditions under which bilinguals and monolinguals can coexist and the ways in which they influence one another over time is also analyzed in current study. This thorough investigation confirms the strength and reliability of the proposed methodology in addressing difficulties associated with language preservation, highlighting its potential for adaptation to other complex fractional language models. Symbolic computation techniques are employed to support and verify the analytic solutions derived.</p>

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Computational modeling of sociolinguistic dynamics: tracing language evolution and preservation in monolingual and bilingual communities

  • 期刊论文

  • 发表日期：

    2025年7月30日

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  • Mubashir Qayyum,
  • Sidra Nayab,
  • Mazhar Hussain,
  • Omar Khan

摘要

Languages develop through a complex interplay of communal competition, shaped by both social and ecological dynamics. While there are thousands of languages spoken globally, many are at risk of disappearing due to changes in language usage and the dominance of more widely spoken languages. Studying and modeling language preservation is crucial, as language directly effects the cultural identity and heritage it represents. This manuscript presents analysis of linguistics dynamics between a bilingual and monolingual population, employing a mathematical model that uses a system of highly non-linear differential equations. For the solution and analysis of the language model, we have applied He-Laplace Carson algorithm by creating multiple homotopies related to the perturbation method. The solution profiles for both the monolinguals as well as bilinguals has been created, which are put to further scrutiny by investigating graphically in detail the prominent parameters such as mass action interaction parameter, language status parameter and immigration rate parameter etc. involved in our model. Furthermore, to ascertain the accuracy and dependability of our proposed method, we have also presented concise and definite numerical validation in all cases involved by finding out the residual errors. Additionally, the fractional parameter is analyzed under different constraints and conditions, with the results presented visually using 2D and 3D plots, as well as gradient contour diagrams. Building on previous mathematical models, our approach incorporates population proportions within a simple structure, resulting in key patterns such as a stable spiral that allows all three language groups to persist. The conditions under which bilinguals and monolinguals can coexist and the ways in which they influence one another over time is also analyzed in current study. This thorough investigation confirms the strength and reliability of the proposed methodology in addressing difficulties associated with language preservation, highlighting its potential for adaptation to other complex fractional language models. Symbolic computation techniques are employed to support and verify the analytic solutions derived.