The activation of behaviour in a daily rhythm governed by the light cycle is a universal phenomenon among humans, laboratory mammals and other vertebrates. For mice, the active period is during the dark. We have quantified the increase in activity when the lights shut off (Light to Dark, L to D) using a generalized CNS arousal assay with 20 ms resolution, rather than traditional running wheels. Data analysis yielded the rare demonstration of an equation which precisely tracks this behavioural transition and, surprisingly, its reverse during D to L. This behavioural dynamic survives in constant darkness (experiment 2) and is hormone-sensitive (experiment 3). Finally (experiment 4), mice on a light schedule analogous to one which proved troublesome for U.S. Navy sailors, had dysregulated activity bursts which did not conform to the transitions between D and L. These experiments show the lawfulness of a behavioural phase transition and the consequence of deviating from that dynamic pattern. And, in a new way, they bring mathematics to the realm of behavioural neuroscience.

由光周期控制的日常节律行为的激活是人类、实验室哺乳动物和其他脊椎动物的普遍现象。对于小鼠来说，活跃期是在黑暗中。我们使用分辨率为 20 ms 的广义 CNS 唤醒试验，而不是传统的跑轮，量化了灯光关闭时活动的增加（从亮到暗，从 L 到 D）。数据分析产生了一个罕见的方程，它精确地跟踪了这种行为转变，令人惊讶的是，它在 D 到 L 期间逆转。这种行为动态在持续的黑暗中生存（实验 2）并且是激素敏感的（实验 3）。最后（实验 4），老鼠在一个类似于被证明对美国海军水手来说很麻烦的光时间表上，具有不符合 D 和 L 之间转换的失调活动爆发。这些实验表明行为相变的合法性以及偏离该动态模式的后果。而且，他们以一种新的方式将数学带入了行为神经科学领域。