Kuramoto Model

A canonical mathematical model of N coupled phase oscillators, each with its own natural frequency, interacting through sinusoidal coupling so that phases evolve according to θ̇_i = ω_i + (K/N)∑_j sin(θ_j − θ_i). It is used to study synchronization transitions and collective phase coherence in heterogeneous oscillator populations.

A mathematical, phase-only model of N coupled oscillators in which each unit i is described by a phase θ_i and natural frequency ω_i and evolves according to dθ_i/dt = ω_i + (K/N) Σ_j sin(θ_j−θ_i).