Abstract
Inspired by language competition processes, we present a model of coupled evolution of node and link states. In particular, we focus on the interplay between the use of a language and the preference or attitude of the speakers towards it, which we model, respectively, as a property of the interactions between speakers (a link state) and as a property of the speakers themselves (a node state). Furthermore, we restrict our attention to the case of two socially equivalent languages and to socially inspired network topologies based on a mechanism of triadic closure. As opposed to most of the previous literature, where language extinction is an inevitable outcome of the dynamics, we find a broad range of possible asymptotic configurations, which we classify as: frozen extinction states, frozen coexistence states, and dynamically trapped coexistence states. Moreover, metastable coexistence states with very long survival times and displaying a non-trivial dynamics are found to be abundant. Interestingly, a system size scaling analysis shows, on the one hand, that the probability of language extinction vanishes exponentially for increasing system sizes and, on the other hand, that the time scale of survival of the non-trivial dynamical metastable states increases linearly with the size of the system. Thus, non-trivial dynamical coexistence is the only possible outcome for large enough systems. Finally, we show how this coexistence is characterized by one of the languages becoming clearly predominant while the other one becomes increasingly confined to ‘ghetto-like’ structures: small groups of bilingual speakers arranged in triangles, with a strong preference for the minority language, and using it for their intra-group interactions while they switch to the predominant language for communications with the rest of the population.
Highlights
Collective social phenomena have traditionally been studied with models based on node states [1]
We address this lack by studying a model where both node and link states are taken into account and characterized by distinct but coupled dynamics
We proposed to consider the use of a language as a property of the interactions between speakers—a link state—and the preference or attitude of the speakers towards it as a property of the speakers themselves—a node state—
Summary
Inspired by language competition processes, we present a model of coupled evolution of node and link licence. Any further distribution of this work must maintain attitude of the speakers towards it, which we model, respectively, as a property of the interactions attribution to the between speakers (a link state) and as a property of the speakers themselves (a node state). Metastable coexistence states with very long survival times and displaying a non-trivial dynamics are found to be abundant. A system size scaling analysis shows, on the one hand, that the probability of language extinction vanishes exponentially for increasing system sizes and, on the other hand, that the time scale of survival of the non-trivial dynamical metastable states increases linearly with the size of the system. Non-trivial dynamical coexistence is the only possible outcome for large enough systems.
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