Shifting Consensus in a Biased Compromise Model

Olivia Cannon, Ty Bondurant, Malindi Whyte, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the effect of bias on the formation and dynamics of opinion clusters in the bounded confidence model. For weak bias, we quantify the change in average opinion and potential dispersion and decrease in cluster size. For nonlinear bias modeling self-incitement, we establish coherent drifting motion of clusters on a background of uniform opinion distribution for biases below a critical threshold where clusters dissolve. Technically, we use geometric singular perturbation theory to derive drift speeds, we rely on a nonlocal center manifold analysis to construct drifting clusters near threshold, and we implement numerical continuation in a forward-backward delay equation to connect asymptotic regimes.

Original languageEnglish (US)
Pages (from-to)297-324
Number of pages28
JournalSIAM Journal on Applied Dynamical Systems
Volume23
Issue number1
DOIs
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2024 Society for Industrial and Applied Mathematics.

Keywords

  • bounded confidence
  • coherent structures
  • lattice dynamical systems
  • nonlocal expansion
  • social dynamics
  • traveling waves

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