Numerical modeling two natural languages interaction

Abstract

In this paper, we propose a mathematical model of the interaction of two languages. In our model, we consider two languages, though it can be generalized to multiple languages, which compete in a heterogeneous environment, consisting of highly varying properties related to the dynamics of the interaction. We use coupled convection–diffusion–reaction equations to describe the processes. Each equation describes the dynamics of one of the languages and contains terms related to the stand-alone dynamics and some coupling terms. The coupling terms represent the interaction between languages. We propose a numerical approach for solving the proposed model equation. In particular, we consider various inhomogeneities associated with cities and countryside, where languages are used differently (e.g., Sakha republic). These dynamics are essential for understanding the evolution of languages (one being dominant) and linguistic ecology that studies languages and their use in real/social life. Because of heterogeneities associated with geography, we use a multiscale approach. The proposed multiscale approach designs special basis functions to represent the small-scale information on larger scales. This way, we can solve the problem on a much coarser grid. Numerical results are presented that describe the dynamics and interaction of two languages. The main novelty of the paper consists of the proposed model and a multiscale algorithm.