Non Trivial Coexistence Conditions for a Model of Language Competition Obtained by Bifurcation Theory

We consider a modification of the model proposed by Abrams and Strogatz to describe the death of a language when it competes with a stronger one within the same community of speakers. The modification opened the possibility of coexistence of both languages under some conditions, but so far it has not been possible to write down the expression of the equilibrium points. In this paper, we nontrivially use bifurcation theory to calculate under which conditions such coexistence arises; namely, we calculate the specific ranges of the parameters that describe the modified model to have this situation, paying special attention to the cases that yield a stable cohabitation of two monolingual populations along with a bilingual one.