Falling asleep follows a predictable bifurcation dynamic.

Sleep is a fundamental part of our lives; yet, how our brain falls asleep remains one of the most enduring mysteries of neuroscience. Here we report a new conceptual framework to analyze and model this phenomenon. The framework represents the changes in brain electroencephalogram activity during the transition into sleep as a trajectory in a normalized feature space. We use the framework to show that the brain's wake-to-sleep transition follows bifurcation dynamics with a distinct tipping point preceded by a critical slowing down. We validate the bifurcation dynamics in two independent datasets, which include more than 1,000 human participants. Finally, we demonstrate the framework's utility by predicting a person's progression into sleep in real time with seconds temporal resolution and over 0.95 average accuracy.