Coupled Oscillators: Kuramoto Synchronization + Chimera States

A population of oscillators, each ticking at its own natural frequency, all nudging each other toward sync. Below a critical coupling they drift apart; above it they fall into step, and the onset lands right where mean-field theory says it should. The second half is stranger. On a ring with a phase lag, identical oscillators can split themselves into a synchronised arc and an incoherent one at the same time. These chimera states are not supposed to exist by symmetry, but they do, and watching one form on the ring is the best part.