English: Visualization of the sleep-wake transition. This video illustrates the change of the evoked response to perturbations, as the model follows the proposed sleep-wake transition depicted in Figure 2. Close to the “wake” state, the system immediately returns to the stable fixed point, without any oscillatory behavior. At the onset of sleep, KNa and σe increase and the system approaches the Hopf bifurcation, such that perturbations away from the active state lead to transient, small and slow oscillatory responses. However, as there are no large deflections, which resemble KCs this regime corresponds to sleep stage N1. Close to label “N2” in Figure 2, KCs emerge as isolated events through a canard explosion (Sleep stage N2). With further transition into deeper sleep, the amplitude of the background oscillations increases and approaches the relaxation cycle of the canard. Finally in the proximity of “N3” in Figure 2 there are no KCs in the sense of isolated events, but large amplitude slow oscillations around a stable focus (Sleep stage N3).