Well posedness and asymptotic consensus in the hegselmann-krause model with finite speed of information propagation

Jan Haskovec

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a variant of the Hegselmann-Krause model of consensus formation where information between agents propagates with a finite speed c > 0. This leads to a system of ordinary differential equations (ODE) with state-dependent delay. Observing that the classical well-posedness theory for ODE systems does not apply, we provide a proof of global existence and uniqueness of solutions of the model. We prove that asymptotic consensus is always reached in the spatially one-dimensional setting of the model, as long as agents travel slower than c. We also provide sufficient conditions for asymptotic consensus in the spatially multidimensional setting.
Original languageEnglish (US)
Pages (from-to)3425-3437
Number of pages13
JournalProceedings of the American Mathematical Society
Volume149
Issue number8
DOIs
StatePublished - May 12 2021

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

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