Topological Flocking — Metric vs Topological Interactions

Vicsek model variants: fixed-radius neighborhood vs fixed-number-of-neighbors alignment

Interaction Mode

Order Parameters

Alignment φ
Mean velocity
ModeMetric
N neighbors avg
Clusters
Metric flocking: interact with all birds within radius r. Collective order fails abruptly at a density-dependent critical noise.

Topological flocking (Ballerini 2008): interact with fixed k nearest neighbors regardless of distance. More robust to perturbations and dilution — matches starling murmurations.