Chimera state (Kuramoto-Battogtokh 2002, Abrams-Strogatz 2004):
dθᵢ/dt = ω − K/N Σⱼ G(i−j) sin(θᵢ−θⱼ+α)
G(x) = (1/2κ) if |x|/N ≤ κ, 0 otherwise (nonlocal kernel).
With α near π/2, the ring spontaneously splits into a synchronized domain (local order r≈1) and an incoherent domain (r≈0). This coexistence was a surprise — such states were thought impossible.