  A formulation of bit-string models of language evolution, based on
differential equations for the population speaking each language, is introduced
and preliminarily studied. Connections with replicator dynamics and diffusion
processes are pointed out. The stability of the dominance state, where most of
the population speaks a single language, is analyzed within a mean-field-like
approximation, while the homogeneous state, where the population is evenly
distributed among languages, can be exactly studied. This analysis discloses
the existence of a bistability region, where dominance coexists with
homogeneity as possible asymptotic states. Numerical resolution of the
differential system validates these findings.
