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How the brain effectively switches between and maintains global states, such as sleep and wakefulness, is not yet understood. We used brainwide functional imaging at single-cell resolution to show that during the developmental stage of lethargus, the Caenorhabditis elegans brain is predisposed to global quiescence, characterized by systemic down-regulation of neuronal activity. Only a few specific neurons are exempt from this effect. In the absence of external arousing cues, this quiescent brain state arises by the convergence of neuronal activities toward a fixed-point attractor embedded in an otherwise dynamic neural state space. We observed efficient spontaneous and sensory-evoked exits from quiescence. Our data support the hypothesis that during global states such as sleep, neuronal networks are drawn to a baseline mode and can be effectively reactivated by signaling from arousing circuits.