Neural Oscillators (2D) — Kuramoto Synchronisation

Presets

Kuramoto Model

N oscillators 30

Coupling K 2.0

Freq spread σ 1.0

Noise level 0.0

Mean freq (Hz) 10

Live Readout

Order r

0.000

Dom. freq

— Hz

Band

—

K_c (critical)

—

How it works

N phase oscillators sit on a flat ring. Each has its own natural frequency ω_i drawn from a spread σ around a mean frequency f0, and is pulled toward the population average phase with strength proportional to the coupling K:

dθi/dt = ωi + K/N · Σj sin(θj − θi) + noise
r = |1/N · Σ e^(iθj)|
Kc = 2 / (π·g(0))

Below the critical coupling K_c the oscillators drift independently and r stays near 0; above it they lock into a shared rhythm and r rises toward 1 — the same synchronisation mechanism believed to underlie EEG brain rhythms. A rolling 512-sample discrete Fourier transform of the population's mean field finds the dominant frequency and classifies it into a band: δ <4Hz, θ <8Hz, α <13Hz, β <30Hz, γ ≥30Hz. Click or drag directly on the ring to kick one oscillator's phase and watch the order parameter dip and re-lock.

Resultant vector (order r) Order r(t) Power spectrum