Clustering and asymptotic behavior in opinion formation

Pierre Emmanuel Jabin, Sebastien Motsch

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


We investigate the long time behavior of models of opinion formation. We consider the case of compactly supported interactions between agents which are also non-symmetric, including for instance the so-called Krause model. Because of the finite range of interaction, convergence to a unique consensus is not expected in general. We are nevertheless able to prove the convergence to a final equilibrium state composed of possibly several local consensus. This result had so far only been conjectured through numerical evidence. Because of the non-symmetry in the model, the analysis is delicate and is performed in two steps: First using entropy estimates to prove the formation of stable clusters and then studying the evolution in each cluster. We study both discrete and continuous in time models and give rates of convergence when those are available.

Original languageEnglish (US)
Pages (from-to)4165-4187
Number of pages23
JournalJournal of Differential Equations
Issue number11
StatePublished - Dec 1 2014


  • Asymptotic analysis
  • Clustering
  • Consensus
  • Krause model
  • Lyapunov function

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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