Phase oscillators with competing communities — synchrony wars on a network
Parameters
Order param r:0.00
Community sync:—
The Kuramoto model with frustration adds a phase offset α to each coupling: dθ_i/dt = ω_i + K/N Σ sin(θ_j−θ_i−α). Frustration (α≠0) creates traveling waves and prevents full synchrony. With multiple communities having strong within-group but weak between-group coupling, cluster synchrony emerges — each group locks internally but the groups drift relative to each other.