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Agent based models of language competition: macroscopic descriptions and order–disorder transitions

AuthorsVázquez, Federico ; Castelló, Xavier ; San Miguel, Maxi
KeywordsStochastic processes
Critical phenomena of socio-economic systems
Interacting agent models
Networks and genealogical trees
Phase transitions: general studies
Fluctuation phenomena, random processes, noise, and Brownian motion
Social and economic systems
Issue DateApr-2010
PublisherInstitute of Physics Publishing
CitationJournal of statistical mechanics (4): P04007 (2010)
AbstractWe investigate the dynamics of two agent based models of language competition. In the first model, each individual can be in one of two possible states, either using language X or language Y, while the second model incorporates a third state XY, representing individuals that use both languages (bilinguals). We analyze the models on complex networks and two-dimensional square lattices by analytical and numerical methods, and show that they exhibit a transition from one-language dominance to language coexistence. We find that the coexistence of languages is more difficult to maintain in the bilinguals model, where the presence of bilinguals facilitates the ultimate dominance of one of the two languages. A stability analysis reveals that the coexistence is more unlikely to happen in poorly connected than in fully connected networks, and that the dominance of just one language is enhanced as the connectivity decreases. This dominance effect is even stronger in a two-dimensional space, where domain coarsening tends to drive the system towards language consensus.
Description30 pages, 11 figures, 1 appendix.-- PDF pre-print.-- http://arxiv.org/abs/1002.1251v1
Publisher version (URL)http://dx.doi.org/10.1088/1742-5468/2010/04/P04007
Appears in Collections:(IFISC) Artículos
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