A chimera state is a paradoxical coexistence of synchronized and desynchronized oscillators in an identical, symmetrically coupled network. The Abrams-Strogatz two-population model shows one coherent + one incoherent group, breaking the symmetry spontaneously.
Two populations (σ,σ): each of size N oscillators. Coupling matrix: [[μ,ν],[ν,μ]] with μ>ν. Chimera: one pop synchronized (|r|≈1), other drifts (|r|≪1). Discovered Kuramoto-Battogtokh 2002.