Fig. 8: Devil’s staircase.
As the natural period is increased for fixed circadian amplitude the number of sleeps per day follows a pattern known as a `Devil’s staircase'. Here this is illustrated for the fixed parameter values χs = 4.2 h, χw = 18.2 h, \({H}_{0}^{-}=\) 0.17, μ = 1 and a = 0.12 by varying the value of the upper threshold \({H}_{0}^{+}\) i.e. taking a horizontal line across Fig. 7a. Note the curvature of the tongues means that the plateau at, for example, Tnat = 1/3 corresponds to 2 sleeps a day. b–f Example raster plots for different values of \({H}_{0}^{+}\).
