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The effects of community structure in the dynamics of language competition

Xavier Castelló 1,  Riitta Toivonen 2,  Víctor M. Eguíluz 1,  Jari Saramäki 2,  Kimmo Kaski 2,  Maxi San Miguel 1

1. Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), Ctra. Valldemossa km. 7,5, Palma de Mallorca E-07122, Spain
2. Laboratory of Computational Engineering, Helsinki University of Technology (HUT), Helsinki 02015, Finland

Abstract
In the general context of dynamics of social consensus, and along the lines of the original proposal by Wang and Minett [1], we study an agent based model for the competition between two socially equivalent languages, addressing the role of bilingualism and social structure. We review our previous results regarding this dynamics on a two-dimensional regular network, where we study the formation of linguistic domains and their interaction across the boundaries; and on a small world network accounting for the effect of long range interactions [2]. In both cases, a final scenario of dominance of one language and extinction of the other is obtained (dominance-extinction state). In comparison with the regular network, smaller times for extinction are found in the small world network.

Looking for an analysis of networks of increasing complexity which account for the main characteristics found in real social networks, we analyze in this work the dynamics on a network with community structure, which also displays presence of hubs, assortativity and high clustering [3]. In the network with communities, although a dominance-extinction state is always reached, the average time for extinction does not give a characteristic time for the dynamics, and metastable states where the two languages coexist, are observed at all time scales [4]. We discuss here how a power law degree distribution of community sizes is sufficient in order to observe this effect.


References:

[1] Wang, W. S.-Y., & Minett, J. W. (2005). The invasion of language: emergence, change and death. Trends in Ecology and Evolution, 20, 263-269.

[2] Castelló, X., Eguíluz, V. M., & San Miguel, M. (2006). Ordering dynamics with two non-excluding options: Bilingualism in language competition. New Journal of Physics, 8, 308–322.

[3] Toivonen, R., Onnela, J., Saramäki, J., Hyvönen, J., Kertész, J., & Kaski, K. (2006). Physica A, 371(2).

[4] Castelló, X., Toivonen, R., Eguíluz, V. M., Saramäki, J., Kaski, K., & San Miguel, M. (2007). Anomalous lifetime distributions and topological traps in ordering dynamics. Europhysics Letters, 79, 66006.

 

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See On-line Journal of International Conference on Economic Science with Heterogeneous Interacting Agents 2008

Submitted: 2008-03-11 16:57
Revised:   2009-06-07 00:48