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Viability and Resilience in the Dynamics of Language Competition

AuthorsCastelló, Xavier ; Vázquez, Federico ; Eguíluz, Víctor M. ; Loureiro-Porto, Lucía; San Miguel, Maxi ; Chapel, Laetitia; Deffuant, Guillaume
Issue Date2011
CitationViability and Resilience of Complex Systems. Concepts, Methods and Case Studies from Ecology and Society 3: 39-74 (2011)
AbstractThis chapter describes the a first case study applying viability based resilience, presented in Chapter 2, on an individual based model (IBM). A particularly sen- sitive issue is to derive macroscopic descriptions from these IBMs, involving a limited number of variables. Indeed, as explained in Chapter 7, this is the con- dition to make tractable the computation of the viability kernel and resilience values. The chapter introduces Individual Based Models (IBMs) of language competition, and explores, through computer simulations, the pattern dynamics of these models and the qualitative role of the prestige and volatility parame- ters. Then it proposes several approaches inspired by physics to perform the derivation of macroscopic descriptions that are able to capture key aspects of the phenomena observed in the IBMs. Finally, it presents an explicit calculation of viability and resilience based on a macroscopic description.
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