A reaction-diffusion model for competing languages

作者：Walters Caroline E^*

来源：Meccanica, 2014, 49(9): 2189-2206.

DOI：10.1007/s11012-014-9973-2

• Language competition
• Reaction-diffusion
• Equilibria
• Nonlinear stability

The extinction of many of the world%26apos;s minority languages is of great concern as language death can lead to the irrevocable loss of cultural information. This often occurs through a process of language shift, where individuals switch from speaking one language to a different, more dominant, language. To prevent the loss of language, it is necessary to determine whether language loss is inevitable or if languages can coexist. We address this question by constructing a nonlinear system of reaction-diffusion equations to model the spread of two competing languages, u and v, which vary temporally and spatially. Language u is assumed to confer a relative status advantage to its speakers, thus individuals may convert from language v to language u. The four constant system equilibria are found. Instability and stability conditions are found for each equilibrium. We conclude that the coexistence of both languages u and v is globally stable, subject to certain constraints on the growth rate of each language and the initial values of both u and v.

• 出版日期2014-9