Abstract
We study the viability and resilience of languages, using a simple dynamical model of two languages in competition. Assuming that public action can modify the prestige of a language in order to avoid language extinction, we analyze two cases: (i) the prestige can only take two values, (ii) it can take any value but its change at each time step is bounded. In both cases, we determine the viability kernel, that is, the set of states for which there exists an action policy maintaining the coexistence of the two languages, and we define such policies. We also study the resilience of the languages and identify configurations from where the system can return to the viability kernel (finite resilience), or where one of the languages is lead to disappear (zero resilience). Within our current framework, the maintenance of a bilingual society is shown to be possible by introducing the prestige of a language as a control variable.
Highlights
The study of language dynamics using computer simulations has become a research field of increasing interest in the scientific community
Models studying language dynamics range from social impact theory applied to language competition [1] to genetic approaches for the evolution of universal grammar [2]
This fact has triggered an effort in order to model and understand the mechanisms within scenarios of language competition: some models study the competition between many languages in order to reproduce the distribution of language sizes in the world in terms of the number of speakers [8,9]; while others focus on the case of language contact between few languages
Summary
The study of language dynamics using computer simulations has become a research field of increasing interest in the scientific community. The need to provide a quantitative analysis in the field of sociolinguistics is getting an increasing attention [7]. This fact has triggered an effort in order to model and understand the mechanisms within scenarios of language competition: some models study the competition between many languages in order to reproduce the distribution of language sizes in the world in terms of the number of speakers [8,9]; while others focus on the case of language contact between few languages (for a review see Refs [10,11]). The model describes the system by aggregated variables that represent the fraction of speakers of each language, where a higher local density of speakers and a higher prestige, the relative status of a language, tend to increase the density of speakers of a language
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