Continuum dynamics of the intention field under weakly cohesive social interaction

Degond, Pierre, Liu, Jian-Guo, Merino-Aceituno, Sara and Tardiveau, Thomas (2017) Continuum dynamics of the intention field under weakly cohesive social interaction. Mathematical Models and Methods in Applied Sciences, 27 (01). pp. 159-182. ISSN 0218-2025

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We investigate the long-time dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. First, we derive a Fokker–Planck-type equation under the assumption that interactions between individuals produce little consensus of opinion (grazing collision approximation). Second, we study conditions under which the Fokker–Planck equation has non-trivial equilibria and derive the macroscopic limit (corresponding to the long-time dynamics and spatially localized interactions) for the evolution of the mean opinion. Finally, we compare two different types of interaction rates: the original one given in the work of Borghesi, Bouchaud and Jensen (symmetric binary interactions) and one inspired from works by Motsch and Tadmor (non-symmetric binary interactions). We show that the first case leads to a conservative model for the density of the mean opinion whereas the second case leads to a non-conservative equation. We also show that the speed at which consensus is reached asymptotically for these two rates has fairly different density dependence.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 20 Feb 2018 09:33
Last Modified: 20 Feb 2018 09:33

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