Math

Kuramoto synchronisation

Watch forty coupled phase oscillators synchronize. Adjust coupling and natural-frequency spread while following individual phases and the complex order parameter.

By Mykhailo Makarov

Actual application image

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Increase coupling to overcome the spread of natural frequencies. The red arrow is the complex phase average; its length R measures coherence.

Equations used in the module

Equations
θi′ = ωi + (K/N) Σj sin(θj−θi)
R exp(iψ) = (1/N) Σj exp(iθj)
0 ≤ R ≤ 1; identical phases give R = 1

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