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Learning thresholds lead to stable language coexistence.

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Summary
This summary is machine-generated.

This study introduces a new language competition model that includes memory and learning effects. The model accurately predicts language shift dynamics, including stable coexistence and initial state preservation, outperforming previous models.

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Area of Science:

  • Sociolinguistics
  • Mathematical Modeling
  • Dynamical Systems

Background:

  • The Abrams-Strogatz model is a foundational framework for understanding language competition.
  • Existing models often lack the capacity to fully capture the nuances of language shift dynamics.

Purpose of the Study:

  • To develop an enhanced language competition model incorporating memory and learning.
  • To analyze the emergent equilibrium states and their stability.
  • To validate the model's predictive power against historical language data.

Main Methods:

  • Extension of the Abrams-Strogatz model to include speaker memory and learning.
  • Mathematical analysis of the model's dynamics, including exact solvability in simplified cases.
  • Numerical simulations to explore model behavior with generalized threshold functions.
  • Comparative analysis of model predictions with real-world historical language datasets.

Main Results:

  • The proposed model predicts novel equilibrium states: stable coexistence of languages and a frozen initial state.
  • These findings hold for both simplified and generalized threshold functions.
  • The enhanced model demonstrates superior fitting to historical language competition data compared to the Abrams-Strogatz model.

Conclusions:

  • Memory and learning are critical factors influencing language shift dynamics.
  • The new model offers a more comprehensive and accurate framework for studying language competition.
  • This work provides valuable insights for understanding and predicting language evolution.