Extending the Abrams-Strogatz Model with a Varying population

This paper extends the Abrams-Strogatz model of language competition by considering population variation over time and the probability of an individual being born as a speaker of one of the two languages. The model is used to analyze Mexican census data, considering the proportion of Bilingual (Spanish and Indigenous) speakers within the Indigenous community. The binomial probability distribution is chosen to measure the likelihood that out of n new Indigenous speakers, k, are born into Bilingual families. This addition complicates the fixed-point analysis of the Abrams-Strogatz model but better reflects the country’s social characteristics.