Neural Oscillator Synchrony — Kuramoto Model

Phase coupling | Spontaneous synchronization | Critical transition

Parameters

Order Parameter R(t)

0.000
K_c = 2Δω/π ≈ —

About

The Kuramoto model: dθᵢ/dt = ωᵢ + (K/N)Σⱼsin(θⱼ−θᵢ). Below the critical coupling K_c = 2Δω/π, oscillators are incoherent (R≈0). Above K_c, they spontaneously synchronize (R→1). This sharp transition appears in fireflies, power grids, neural gamma oscillations, and cardiac pacemaker cells.