Coupled oscillator network (Kuramoto / XY model)

A network of identical oscillators — pendula, LC circuits, or CMOS ring oscillators — coupled to their neighbours by springs or resistive links. The Kuramoto model describes how each oscillator's phase evolves under the pull of its neighbours. When the coupling weights encode a graph's edge weights, the system's stable phase configuration minimizes the same energy function as MAX-CUT: oscillators partition into two phase-locked clusters (0° and 180°) that approximately bisect the graph. Implemented in silicon as oscillator-based Ising machines with up to 1440 CMOS nodes; reported within 99% of optimal MAX-CUT on tested benchmarks. Speed: microseconds to milliseconds (oscillator ring-down time). Capacity: graph problems with hundreds to thousands of nodes.