Analytical approach to bit-string models of language evolution

TL;DR

This paper introduces a differential equation-based framework for modeling language evolution using bit-strings, analyzing stability and coexistence of dominant and homogeneous language states with numerical validation.

Contribution

It presents a novel differential equations formulation for language evolution models and explores their stability and bifurcation properties.

Findings

Existence of a bistability region with coexistence of dominance and homogeneity.

Stability analysis of the dominance state and exact study of the homogeneous state.

Numerical simulations confirm theoretical predictions.

Abstract

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.