A Model of Competition Among More than Two Languages

Ryo Fujie*, Kazuyuki Aihara, Naoki Masuda


研究成果: Article査読

5 被引用数 (Scopus)


We extend the Abrams-Strogatz model for competition between two languages (Abrams and Strogatz in Nature 424:900, 2003) to the case of n (≥2) competing states (i. e., languages). Although the Abrams-Strogatz model for n=2 can be interpreted as modeling either majority preference or minority aversion, the two mechanisms are distinct when n≥3. We find that the condition for the coexistence of different states is independent of n under the pure majority preference, whereas it depends on n under the pure minority aversion. We also show that the stable coexistence equilibrium and stable monopoly equilibria can be multistable under the minority aversion and not under the majority preference. Furthermore, we obtain the phase diagram of the model when the effects of the majority preference and minority aversion are mixed, under the condition that different states have the same attractiveness. We show that the multistability is a generic property of the model facilitated by large n.

ジャーナルJournal of Statistical Physics
出版ステータスPublished - 2013 4月

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学


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