Input

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Sleep model

The Sleep Cycle App provides graphs to the user that show his measured sleep behavior during that night. Here's an example:

To model this pattern, we assumed that the peaks and valleys of the graph are sinusoidal with random periods, amplitudes and equilibriums. Furthermore, we made the assumption that the period is normally distributed with mean 90 minutes or 5400 seconds (mean duration of one sleep cycle) and standard deviation 30 minutes or 1800 seconds.

globals [y
         Tgem
         start
         T
         p
         rc
         x
         R
         time
         stage
         test]

to Setup
  clear-all
  set y 100
  set Tgem (90 * 60)
  reset-ticks
end

to Go
  foreach [1 2] [
    set start y
    set T -1
    while [T < 0] [set T (random-normal Tgem 1800)]
    set p (random-float 1.0)
    set rc (4 / (1 + exp((ticks - (2.5 * Tgem)) / 20000)) - 2)
    ifelse rc > 0
      [set x (0.5 - (1 / rc) + sqrt((2.0 / rc) * p + (rc ^ -2) - (rc ^ -1) + 0.25))]
      [set x (0.5 - (1 / rc) - sqrt((2.0 / rc) * p + (rc ^ -2) - (rc ^ -1) + 0.25))]
    ifelse ? = 1
      [set R (x * start / 2)]
      [set R ((x - 1) * (100 - start) / 2)]
    set time (n-values (T / 2) [?])
    foreach time [
      set y (R * (cos (360 * ? / T)) + start - R)
      set stage ((y - (y mod 25)) / 25 - 3)
      set test (1 / (1 + exp(ticks)))
      tick
    ]
  ]
end