Bounded confidence model: consensus vs fragmentation transition
Clusters: —
The Deffuant–Weisbuch (DW) model: N=200 agents hold opinions in [0,1].
At each step, a random pair (i,j) meets; if |xᵢ − xⱼ| < ε, both update:
xᵢ ← xᵢ + μ(xⱼ − xᵢ), xⱼ ← xⱼ + μ(xᵢ − xⱼ).
Critical threshold: ε ≈ 1/(2k) gives k clusters. Above ε ≈ 0.5: full consensus.
Below: fragmentation into multiple opinion clusters. Top panel: space-time trajectories. Bottom: final histogram.