Analytical approach to bit-string models of language evolution

Details Analytical approach to bit-string models of language evolution Analytical approach to bit-string models of language evolution

2007-11-08

arxiv.org/abs/0711.1360v1

Physics

Physics and Society

To appear in Int. J. Mod. Phys. C

Scientific paper

10.1142/S0129183108012340

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.

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