# Research of the Dynamic System Describing Globalization Process

## Abstract

In this paper, we consider a new nonlinear continuous mathematical model of linguistic globalization. Two categories of the world’s population are considered: a category that hinders and a category conducive to the dominant position of the English language.With a positive demographic factor of the population, which prevents globalization and the negative demographic factor of the population contributing to globalization, it is shown that the dynamic system describing this process allows for the existence of two topologically not equivalent phase portraits (a stable node, a limit cycle). Under certain restrictions on the parameters of the model, the theorem on the absence of periodic trajectories of the dynamical system is proved and an asymptotically stable equilibrium position (limit cycle) is found. Thus, it is established that complete linguistic globalization is impossible if the demographic factor of the category of the world population contributing to the dominance of the English language is non-positive. Full linguistic globalization is possible only if the demographic factor is positive for the category of the world’s population, which contributes to the dominance of the English language and a certain restriction on the parameters of the model associated with the coefficient of assimilation.

## Keywords

Nonlinear mathematical model of linguistic globalization Dynamical system Asymptotically stable equilibrium position Linguistic globalization## References

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