Kuramoto model: synchronisation and complex systems.

Originally a numerical assignment for the Introduction to Complex Systems course at Utrecht University, reworked into a single companion notebook, kuramoto_notebook.ipynb, which reproduces the following numerical studies:

1. Two dynamical regimes: $r(t)$ below and above the critical coupling $K_c$
2. Sensitivity to initial conditions: fixed $\omega$ vs. fixed $\theta(0)$
3. Phase transition for Gaussian frequencies: $r_\infty$ vs. $K$ against the self-consistency equation, $K_c = 2\sqrt{2/\pi}$
4. Phase transition for uniform frequencies: same, with $K_c = 2/\pi$
5. Kuramoto model on Watts-Strogatz networks: $K_c$ as a function of the rewiring probability $p$

figures/ contains the figures generated by running the notebook.

All simulations use a vectorised mean-field reduction (the $O(N^2)$ pairwise coupling is replaced by the complex order parameter $re^{i\psi}$), and the Watts-Strogatz networks are generated on the fly with networkx.