Dynamics of two languages competing on a network: a case study

A language dynamics model on a square lattice, which is an extension of the one popularized by Abrams and Strogatz [1], is analyzed using ODE bifurcation theory. For this model we are interested in the existence and spectral stability of structures such as stripes, which are realized through pulses and/or the concatenation of fronts, and spots, which are a contiguous collection of sites in which one language is dominant. Because the coupling between sites is nonlinear, the boundary between sites containing speaking two different languages is"sharp"; in particular, in a PDE approximation it allows for the existence of compactly supported pulses (compactons). The dynamics are considered as a function of the prestige of a language. In particular, it is seen that as the prestige varies, it allows for a language to spread through the network, or conversely for its demise.

• Publication year

  2021

• Venue

  Unknown venue

• Publication date

  2021-02-14

• Fields of study

  Physics

• Identifiers
  arXiv 2102.07220
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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