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arXiv 1206.4557physics.soc-phcond-mat.stat-mechcs.SI
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两种以上语言竞争的模式

A model of competition among more than two languages

Ryo Fujie, Kazuyuki Aihara, Naoki Masuda

摘要:

我们将两种语言之间竞争的Abrams-Strogatz模型[Nature 424,900(2003)]扩展到n(>=2)个竞争状态的情况(即,语言)。虽然n=2的Abrams-Strogatz模型可以解释为多数偏好或少数厌恶的模型,但当n>=3时,这两种机制是不同的。我们发现,在纯多数偏好下,不同状态共存的条件与n无关,而在纯少数厌恶下,不同状态共存的条件与n有关。我们还证明了稳定共存均衡和稳定垄断均衡在少数人厌恶下是多稳定的,而在多数人偏好下不是。在不同状态具有相同吸引力的条件下,得到了混合多数偏好和少数厌恶效应时模型的相图。我们表明,多稳定性是一个通用的属性的模型促进大n。

英文摘要:

We extend the Abrams-Strogatz model for competition between two languages [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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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