Every night, the brain cycles through several sleep stages — from drowsiness to deep sleep and back. Some transitions happen abruptly, like a light switch flipping, while others are smooth, like a slow slide down a slope. A team of researchers has built a mathematical model that describes these transitions as a ball moving across a changing landscape of hills and valleys.

At the core of the model is the idea of a hidden coordinate — a parameter reflecting the overall orderliness of neural activity. This coordinate is extracted from EEG seizure detection data (recordings of the brain's electrical activity) using a special procedure to avoid self-fulfilling prophecies. As the coordinate changes, the landscape reshapes: new attractor basins appear where activity settles, along with barriers between them. For example, falling asleep is like the basin of wakefulness disappearing — the brain loses stability and tumbles into the state of Neural Network Oscillations sleep.

The authors modeled six types of transitions, from sharp bifurcations to smooth crossovers. Computer simulations showed how the correlation length grows — the distance over which neurons behave in concert. Larger and larger brain regions become involved. This is a key prediction that sets the model apart from simpler ones. In a blind experiment, the algorithm could partially distinguish transition archetypes with 49% accuracy (random guessing would give 17%).

For now, it's a theoretical scaffold awaiting validation against real recordings. If the predictions hold up, we'll gain a tool for precisely describing sleep disruptions — for instance, why falling asleep with insomnia becomes a painful climb over a ridge rather than a gentle descent.