Coexistence in exotic scenarios of a modified Abrams-Strogatz model

We work on a model that has succeeded in describing real cases of coexistence of two languages within a closed community of speakers, taking into account bilingualism and incorporating a parameter to measure the distance between languages. The dynamics of this model depend on a characteristic exponent, which weighs the power of the size of a group of speakers to attract new members. So far, this model had been solved only when this characteristic exponent is greater than 1. In this article, we have managed to solve the nature of the stability of all the possible situations for this characteristic exponent, that is, when it is less or equal than 1 and covering also the situations produced when it is 0 or negative. We interpret these new situations and find that, even in such exotic scenarios, there are configurations of the resulting societies where all the languages coexist