学习阈值导致稳定的语言共存
Learning thresholds lead to stable language coexistence
AI总结：
该研究基于Abrams-Strogatz模型提出纳入记忆和学习影响的语言竞争模型，通过阈值函数实现两种语言的稳定动态共存等新平衡状态，数值验证其普适性且与历史数据拟合良好。
摘要：
我们提出了一种基于Abrams-Strogatz模型的语言竞争模型，该模型在语言转换动力学中纳入了记忆和学习的影响。在粗粒化时间尺度上，记忆和学习的影响可表示为竞争语言使用者比例的阈值。最简形式下，所得模型可精确求解。除了两种语言之一达成共识的状态外，该模型还描述了Abrams-Strogatz模型中不存在的额外平衡状态：两种语言的稳定动态共存，以及与初始状态一致的冻结状态。我们通过数值方法表明，这些结果对于更一般形式的阈值函数仍然成立。将模型预测与历史数据集比较后发现，虽然Abrams-Strogatz模型无法描述某些相关语言竞争情况，但所提出的模型拟合效果良好。
英文摘要：
We introduce a language competition model that is based on the Abrams-Strogatz model and incorporates the effects of memory and learning in the language shift dynamics. On a coarse grained time scale, the effects of memory and learning can be expressed as thresholds on the speakers fractions of the competing languages. In its simplest form, the resulting model is exactly solvable. Besides the consensus on one of the two languages, the model describes additional equilibrium states that are not present in the Abrams-Strogatz model: a stable dynamical coexistence of the two languages and a frozen state coinciding with the initial state. We show numerically that these results are preserved for threshold functions of a more general shape. The comparison of the model predictions with historical datasets demonstrates that while the Abrams-Strogatz model fails to describe some relevant language competition situations, the proposed model provides a good fitting.
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