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Systems of globally coupled oscillators often display states of full synchrony in which all oscillators are phase locked. It is shown that for globally coupled oscillators with neuronlike pulse interactions, the phase-locked state is unstable to inhomogeneity in the local frequency. For weak inhomogeneity the system breaks into two subpopulations: one that is phase locked and another one that consists of aperiodic oscillators. The fraction of the unlocked population remains finite in the limit of vanishing inhomogeneity.
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