Math @ Duke

Publications [#323838] of JianGuo Liu
Papers Published
 Degond, P; Liu, JG; MerinoAceituno, S; Tardiveau, T, Continuum dynamics of the intention field under weakly cohesive social interaction,
Mathematical Models and Methods in Applied Sciences, vol. 27 no. 1
(January, 2017),
pp. 159182, World Scientific Pub Co Pte Lt [doi]
(last updated on 2019/06/19)
Abstract: © 2017 The Author(s). We investigate the longTime dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. First, we derive a FokkerPlanckType equation under the assumption that interactions between individuals produce little consensus of opinion (grazing collision approximation). Second, we study conditions under which the FokkerPlanck equation has nonTrivial equilibria and derive the macroscopic limit (corresponding to the longTime 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 (nonsymmetric 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 nonconservative equation. We also show that the speed at which consensus is reached asymptotically for these two rates has fairly different density dependence.


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