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Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked
oscillators coexist with drifting ones. Discovered two years ago, such ‘‘chimera states’’ are believed to
be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of
nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators
coupled by a cosine kernel.We show that the stable chimera state bifurcates from a spatially modulated
drift state, and dies in a saddle-node bifurcation with an unstable chimera state.sm29
