Capturing the non-stationarity of whole-brain dynamics underlying human brain states

•Brain dynamics depicts a complex energy landscape that changes over time.•We approximate the energy landscape of brain dynamics underlying different states.•Measure of consciousness through variability of attractors of human fMRI signals.•A new tool, the Model transform, applies simple models to complex systems. Brain dynamics depicts an extremely complex energy landscape that changes over time, and its characterisation is a central unsolved problem in neuroscience. We approximate the non-stationary landscape sustained by the human brain through a novel mathematical formalism that allows us characterise the attractor structure, i.e. the stationary points and their connections. Due to its time-varying nature, the structure of the global attractor and the corresponding number of energy levels changes over time. We apply this formalism to distinguish quantitatively between the different human brain states of wakefulness and different stages of sleep, as a step towards future clinical applications.