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.

大脑动力学描绘了一个随时间变化的极其复杂的能量景观，其表征是神经科学中一个未解决的核心问题。我们通过一种新颖的数学形式来近似人脑维持的非平稳景观，该数学形式使我们能够表征吸引子结构，即静止点及其连接。由于其随时间变化的性质，全局吸引子的结构和相应的能级数量随时间而变化。我们应用这种形式来定量区分不同的人类大脑清醒状态和不同的睡眠阶段，作为迈向未来临床应用的一步。