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Viability and Resilience in the Dynamics of Language Competition

Castelló, Xavier; Vazquez, Federico; Eguíluz, Víctor M.; Loureiro-Porto, Lucía; San Miguel, Maxi; Chapel, Laetitia; Deffuant, Guilaume
Viability and Resilience of Complex Systems. Concepts, Methods and Case Studies from Ecology and Society. G. Deffuant and N. Gilbert, eds. , Springer 39-74 (2011)

This chapter describes a first case study applying viability based resilience, presented in Chapter 2, on an individual based model (IBM). A particularly sensitive issue is to derive macroscopic descriptions from these IBMs, involving a limited number of variables. Indeed, as explained in Chapter 7, this is the condition 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 parameters. 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.