Kuramoto model:\( \dfrac{d\theta_i}{dt} = \omega_i + \dfrac{K}{D N} \sum_{j} A_{ij}\,\sin(\theta_j - \theta_i) \)\( r = \dfrac{1}{N}\left|\sum_j e^{i \theta_j}\right| \)

\( N \) - network size
\( D \) - density
\( \langle \omega \rangle \) - mean frequency
\( \sigma_{\omega} \) - frequency std. deviation
\( K \) - coupling strength
Speed x0

Built by Guram Mikaberidze.

Network

\(\theta\) - node phases
\(+\pi\)
0
\(-\pi\)

Phase circle

Order parameter
\(\omega\) - node frequencies
\(\langle \omega \rangle + 2\sigma_{\omega}\)
\(\langle \omega \rangle\)
\(\langle \omega \rangle - 2\sigma_{\omega}\)
\( K_c = 2 \sigma_{\omega} \sqrt{2/\pi} \approx 0 \)