Continuum dynamics of the intention field under weakly cohesive social interaction

Pierre Degond South Kensington Campus, Jian-Guo Liu Department of Physics, Duke University Sara Merino-Aceituno South Kensington Campus Thomas Tardiveau Ecole Polytechnique, Route de Saclay

Analysis of PDEs mathscidoc:1702.03014

Mathematical Models and Methods in Applied Sciences, 27, (1), 159-182, 2017.1
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.
Opinion formation; grazing limit; non-symmetric rate; continuum limit; Deffuant–Weisbuch model
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@inproceedings{pierre2017continuum,
  title={Continuum dynamics of the intention field under weakly cohesive social interaction},
  author={Pierre Degond, Jian-Guo Liu, Sara Merino-Aceituno, and Thomas Tardiveau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170206162209551049200},
  booktitle={Mathematical Models and Methods in Applied Sciences},
  volume={27},
  number={1},
  pages={159-182},
  year={2017},
}
Pierre Degond, Jian-Guo Liu, Sara Merino-Aceituno, and Thomas Tardiveau. Continuum dynamics of the intention field under weakly cohesive social interaction. 2017. Vol. 27. In Mathematical Models and Methods in Applied Sciences. pp.159-182. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170206162209551049200.
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