Continuum dynamics of the intention field under weakly cohesive social interaction
© 2017 The Author(s). 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.
Degond, P; Liu, JG; Merino-Aceituno, S; Tardiveau, T
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