Modeling language shift

Abstract

National Academy of Science

Exact Solutions of a Mathematical Model Describing Competition and Co-Existence of Different Language Speakers

“…As a result, four exact solutions in explicit form were found for the first time. One of them (see formulae (11)) was studied in detail in order to identify its properties. Having this done, plots of the traveling fronts were drown and the relevant interpretation describing the language shift that occurred in Ukraine during the Soviet times was suggested.…”

“…In this section, we study in detail exact solution (11). First of all, we answer the question: When do positive coefficients d 1 , d 3 , α 2 , α 4 and µ lead automatically to positive values of α 1 , α 3 , β 1 , β 3 , κ 1 and κ 2 in formulae (12)?…”

“…Thus, we can use the formulae derived above in order to construct examples of traveling fronts to plot the relevant curves (using the package Maple) and to present their plausible interpretation. Figures 1-3 represent the exact solution (11) in Case (i) µ > 0 (Figures 1 and 2) and Case (ii) µ < 0 (Figure 3). All the curves satisfy the natural requirement of positivity at the given space intervals.…”

“…On the other hand, the rigorous mathematical models came to social sciences and humanities only recently. In particular, papers devoted to rigorous mathematical modeling interaction of communities (populations) of different language speakers were published only during the last two decades [5][6][7][8][9][10][11]. These models are based on nonlinear differential equations of reaction-diffusion type.…”

Revisit Language Modeling Competition and Extinction: A Data-Driven Validation

“…Macroscopic models of language competition treat the population as homogeneous (all members are the same, and evenly dispersed in an area) and fully connected (all members interact with other members) [5]. These macroscopic models are usually described by differential equations.…”