Learning thresholds lead to stable language coexistence

Abstract

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.

15 pages, 6 figures and 1 table

References in corpus (11)

• Fast unfolding of communities in large networks
• Ordering dynamics with two non-excluding options: Bilingualism in language competition
• Topology Induced Coarsening in Language Games
• Interlinguistic similarity and language death dynamics
• Influence of geography on language competition
• A mathematical model of social group competition with application to the growth of religious non-affiliation
• Modeling two-language competition dynamics
• Threshold $q$-voter model
• Threshold learning dynamics in social networks
• The evolution of polarization in the legislative branch of government
• Infection patterns in simple and complex contagion processes on networks