We introduce a language competition model that incorporates the effects of
memory and learning on the language shift dynamics, using the Abrams-Strogatz
model as a starting point. On a coarse grained time scale, the effects of
memory and learning can be expressed as thresholds on the speakers fractions.
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
coexistence of the two languages, if both thresholds are low enough, so that
the language shift processes in the two opposite directions compensate each
other, and a frozen state coinciding with the initial state, when both
thresholds are too high for any language shift to take place. We show
numerically that these results are preserved for threshold functions of a more
general shape.

该研究提出了一种语言竞争模型，该模型充分考虑了记忆和学习对语言转移动态的影响，通过使用 Abrams-Strogatz 模型作为起点。模型以讲话者比例的阈值来表达记忆和学习的效应，在最简单的形式下，该模型是可解的。除了两种语言中的共识外，该模型还描述了 Abrams-Strogatz 模型中不存在的其他平衡状态：如果两个阈值都足够低，使得两个相反方向上的语言转移过程相互抵消，将出现两种语言的稳定共存；同时，当这两个阈值对于任何语言转移来说都太高时，将出现与初始状态相符的冻结状态。我们通过数值模拟证明了这些结果在阈值函数形状更一般的情况下仍然成立。