Social media enhances languages differentiation: a mathematical description

Vidal-Franco, Ignacio; Guiu-Souto, Jacobo; Muñuzuri, Alberto P.

doi:10.1098/rsos.170094

Cited by 11 publications

(11 citation statements)

References 30 publications

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“…To incorporate this into the model, we modified Eq. (1) into the simplest ones that include some interaction across regions 37 :Network nodes (i.e., Galician regions) are still labeled by i = 1, ..., N = 20. Variables x i and y i still represent fractions of monolingual Galician and Spanish speakers within each region.…”

Section: Resultsmentioning

confidence: 99%

Urbanity and the dynamics of language shift in Galicia

et al. 2019

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Sociolinguistic phenomena often involve interactions across different scales and result in social and linguistic changes that can be tracked over time. Here, we focus on the dynamics of language shift in Galicia, a bilingual community in northwest Spain. Using historical data on Galician and Spanish speakers, we show that the rate at which shift dynamics unfold correlates inversely with the internal complexity of a region (approximated by the proportion of urban area). Less complex areas converge faster to steady states, while more complex ones sustain transitory dynamics longer. We further explore the contextual relevance of each region within the network of regions that constitute Galicia. The network is observed to sustain or reverse the dynamic rates. This model can introduce a competition between the internal complexity of a region and its contextual relevance in the network. Harnessing these sociodynamic features may prove useful in policy making to limit conflicts.

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Section: Resultsmentioning

confidence: 99%

Urbanity and the dynamics of language shift in Galicia

et al. 2019

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“…As the rate of antagonistic opinions spread faster relative to mutualistic ones, the hierarchical structure is lost and while multiple opinions form, they are stochastic with respect to the population on which the information is spreading. Of course, similar considerations apply when modeling ecological species [25] or linguistic adoption [22]. The general form of the differential equations used here are,…”

Section: Discussionmentioning

confidence: 99%

“…, by increasing the connectivity of the network [22]. However the effect is far more nuanced as shown in Fig.…”

Section: Introductionmentioning

confidence: 93%

“…Turing patterns have also been observed in more exotic variants of network topologies, such as directed, multiplex and time-evolving networks [15][16][17]. Indeed, given the widespread prevalence of networks across a plethora of socioeconomic, biological and technological systems [18][19][20][21], the developed framework is being used to model interesting dynamical phenomena; in [22], predator-prey [23] dynamics is used along with cross-diffusion (in addition to ordinary diffusion), to model the evolution of two competing languages on a scale free network [24]. In [25] three species interactions are used to model ecological meta-populations where concentrations correspond to the population densities of species in a food web.…”

Section: Introductionmentioning

confidence: 99%

“…A similar set of equations can be used if the system is not continuous but instead is composed of N independent nodes that interact via diffusive transport over m edges [12,14,22,37]. The analog of the operator ∇ 2 is now the Laplacian matrix,…”

Section: Introductionmentioning

confidence: 99%

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Turing patterns mediated by network topology in homogeneous active systems

et al. 2019

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Mechanisms of pattern formation-of which the Turing instability is an archetype-constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing instability can induce pattern formation in discrete media such as complex networks, opening up the intriguing possibility of exploring it as a generative mechanism in a plethora of socioeconomic contexts. Yet, much remains to be understood in terms of the precise connection between network topology and its role in inducing the patterns. Here, we present a general mathematical description of a two-species reaction-diffusion process occurring on different flavors of network topology. The dynamical equations are of the predator-prey class, that while traditionally used to model species population, has also been used to model competition between antagonistic ideas in social systems. We demonstrate that the Turing instability can be induced in any network topology, by tuning the diffusion of the competing species, or by altering network connectivity. The extent to which the emergent patterns reflect topological properties is determined by a complex interplay between the diffusion coefficients and the localization properties of the eigenvectors of the graph Laplacian. We find that networks with large degree fluctuations tend to have stable patterns over the space of initial perturbations, whereas patterns in more homogenous networks are purely stochastic. arXiv:1903.03845v1 [cond-mat.dis-nn]

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