§9 Kuramoto Model — Synchronization of Phase Oscillators
dθi/dt = ωi + (K/N) · Σj sin(θj - θi)
R · eiψ = (1/N) · Σj eiθj
R · eiψ = (1/N) · Σj eiθj
The Kuramoto model describes how N phase oscillators synchronize through global coupling. The order parameter R measures the degree of synchronization: R ≈ 0 is a desynchronized state, R ≈ 1 is full synchronization. When the coupling strength K exceeds a critical value, the system undergoes a continuous phase transition from desynchronization to synchronization.
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