Kuramoto Synchronization

N=50 coupled oscillators — phase transitions in coupled dynamics

dθᵢ/dt = ωᵢ + (K/N)Σⱼ sin(θⱼ−θᵢ) | Order parameter r(t) = |⟨e^{iθ}⟩| | Critical coupling K_c = 2/πg(0) where g is freq distribution