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Coupled dynamics of node and link states in complex networks: a model for language competition

Authors: Carro, A; Toral, R; Miguel, MS;

Coupled dynamics of node and link states in complex networks: a model for language competition

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.

21 pages, 15 figures

Countries
United Kingdom, Spain
Keywords

Social and Information Networks (cs.SI), FOS: Computer and information sciences, Physics - Physics and Society, Statistical Mechanics (cond-mat.stat-mech), Science, Physics, QC1-999, Q, FOS: Physical sciences, agent-based modeling, Computer Science - Social and Information Networks, complex networks, Physics and Society (physics.soc-ph), Nonlinear Sciences - Adaptation and Self-Organizing Systems, language dynamics, social systems, Adaptation and Self-Organizing Systems (nlin.AO), language competition, Condensed Matter - Statistical Mechanics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
views
OpenAIRE UsageCountsViews provided by UsageCounts
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15
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