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Kuramoto Model

Synchronisation de phase par couplage non-linéaire

Kuramoto, 1975

Kuramoto Oscillators

Phase synchronization network

Parameters

Coupling (K)1.0
Oscillators10

State

Order Parameter (r)0.0000
Mean Field ψ0.0000
Mean Field θ0.0000

Mathematics

Dynamics:

dϕi/dt=ωi+KN∑j=1Nsin⁡(ϕj−ϕi)d\phi_i/dt = \omega_i + \frac{K}{N} \sum_{j=1}^{N} \sin(\phi_j - \phi_i)

Mean Field:

r⋅eiψ=1N∑j=1Neiϕjr \cdot e^{i\psi} = \frac{1}{N} \sum_{j=1}^{N} e^{i\phi_j}

Order Parameter:

r=∣1N∑j=1Neiϕj∣r = \left| \frac{1}{N} \sum_{j=1}^{N} e^{i\phi_j} \right|