Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics



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BibTex format

author = {Degond, P and Liu, J-G and Merino-Aceituno, S and Tardiveau, T},
doi = {10.1142/S021820251740005X},
journal = {Mathematical Models and Methods in Applied Sciences},
title = {Continuum dynamics of the intention field under weakly cohesive social interaction},
url = {},
volume = {27},
year = {2017}

RIS format (EndNote, RefMan)

AB - 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.
AU - Degond,P
AU - Liu,J-G
AU - Merino-Aceituno,S
AU - Tardiveau,T
DO - 10.1142/S021820251740005X
PY - 2017///
SN - 1793-6314
TI - Continuum dynamics of the intention field under weakly cohesive social interaction
T2 - Mathematical Models and Methods in Applied Sciences
UR -
UR -
VL - 27
ER -