包含双语状态的语言竞争阈值模型
Threshold model of language competition including the bilingual state
AI总结：
本文提出一种包含双语状态的语言竞争阈值模型，通过引入阈值机制，研究了语言竞争的动态行为，揭示了多种平衡状态，包括共存状态。
摘要：
我们提出了一种包含中间双语状态的语言竞争阈值模型。该模型基于Minett-Wang模型，但通过在语言转换率中引入阈值，纳入了记忆和学习的影响。该模型是分段线性的，允许精确的解析处理。我们研究了对称情况，其中两种竞争语言在地位和社会压力方面是等同的，并提供了各种动态制度的完整列表。我们还研究了几种极限情况，对应于不对称系统，并刻画了所有可能的渐近行为谱。与Minett-Wang模型不同，后者总是预测一种语言的灭绝，所提出的新型模型表现出广泛的平衡场景，包括共存的平衡状态。在大多数共存制度中，少数语言使用者要么完全单语，要么完全双语。
英文摘要：
We propose a threshold model of language competition which includes intermediate bilingual state. The model is based on the Minett-Wang model but through the introduction of thresholds in the language shift rates it incorporates the effects of memory and learning. The model is piecewise-linear, allowing the exact analytical treatment. We study the symmetric case where two competing languages are equivalent in terms of status and social pressure and provide a complete list of the various dynamical regimes. We also study several limiting regimes corresponding to asymmetric systems and characterize the full spectrum of possible asymptotic behaviors. Unlike the Minett-Wang model, which always predicts the extinction of one of the languages, the proposed new model exhibits a wide range of possible equilibrium scenarios, including equilibrium states of coexistence. Most commonly, in such coexistence regimes the minority language speakers are either completely monolingual or completely bilingual.
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