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Continuum dynamics of the intention field under weakly cohesive social interaction

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posted on 2023-06-09, 12:14 authored by Pierre Degond, Jian-Guo Liu, Sara Merino-Aceituno, Thomas Tardiveau
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Mathematical Models and Methods in Applied Sciences

ISSN

0218-2025

Publisher

World Scientific Publishing

Issue

01

Volume

27

Page range

159-182

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-02-20

First Open Access (FOA) Date

2018-02-20

First Compliant Deposit (FCD) Date

2018-02-19

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