Chimera states — first described by Kuramoto & Battogtokh (2002), named by Abrams & Strogatz (2004) — are remarkable solutions where
identical oscillators split into synchronized and incoherent clusters with no obvious symmetry breaking.
dθi/dt = ω − K/(2R·N) Σ|i−j|≤RN sin(θi−θj+α)
Key ingredients:
nonlocal coupling (range r),
phase lag α ≈ π/2. Top: phases on ring (hue). Middle: phase velocity space-time (bright=fast/incoherent). Bottom: local order parameter R(x) — chimera shows R≈1 (sync) in one region and R<1 (incoherent) elsewhere.