Explosive Synchronization

First-order sync transition on scale-free networks — abrupt, irreversible, hysteresis

Oscillator Network

Order Parameter

R (Kuramoto):
Mean ψ: °
Sync clusters:
Sweeping K: idle
Explosive sync (Gómez-Gardeñes 2011): assigning ω_i ∝ k_i (degree) to Kuramoto oscillators on scale-free nets yields a first-order transition with hysteresis, unlike classical Kuramoto (2nd order). Mechanism: high-degree hubs synchronize last, then trigger avalanche. Observed in: brain cortex, power grids.