Fig. 6: Natural period of the sleep-wake oscillator.
a The two-process model (2pm) with the circadian amplitude set to zero. For the standard parameters (χs = 4.2 h, χw = 18.2 h, \({H}_{0}^{+}=\) 0.67, \({H}_{0}^{-}=\) 0.17, μ = 1) the period of the sleep-wake cycle is approximately 22.6 h, of which approximately 5.8 h is sleep ( ~ 26%). The righthand panel shows a raster plot with the timing of sleep on successive 24 h days. b–h Illustration of the dependence of the natural period on the parameters in the 2pm, as given by equations (1)-(3). The vertical red line indicates the position of the standard parameters. Since it is sometimes useful to describe the position of the thresholds by a mean value and the separation instead of an upper and lower value, we have shown the dependence of sleep and wake duration on the value of the upper threshold \({H}_{0}^{+}\), the value of the lower threshold \({H}_{0}^{-}\) and also the mean level of the thresholds \(({H}_{0}^{+}+{H}_{0}^{-})/2\) and the separation of the thresholds \({H}_{0}^{+}-{H}_{0}^{-}\).
