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. 2014 Aug 1;9(8):e103877. doi: 10.1371/journal.pone.0103877

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© 2014 Skeldon et al

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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(a) A single trajectory of the two-process model showing successive times of sleep onset. (b) Trajectories of the two-process model for different initial sleep onset times. Each different sleep onset time results in a different sequence, , but each sequence rapidly converges to the same sleep onset time, of modulo 1 day. (c) A zoom of (b), showing only the trajectories for and (d) First return map for the two-process model. The black line shows the return map, in other words for any value of sleep onset time on day , it shows the onset time of sleep on day , . The grey diagonal line is the line along which . One typical trajectory is plotted for showing the rapid convergence to the periodic cycle where modulo 1 day, the point at which the return map and the diagonal line intersect. The discontinuity is a result of the fact that neighbouring values of exist that lead to very different values for , as shown in (c). Parameter values for the two-process model are based on the PR model for the human sleep-wake cycle and can be found in (15).

Inline graphic — (a) A single trajectory of the two-process model showing successive times of sleep onset. (b) Trajectories of the two-process model for different initial sleep onset times. Each different sleep onset time results in a different sequence, , but each sequence rapidly converges to the same sleep onset time, of modulo 1 day. (c) A zoom of (b), showing only the trajectories for and (d) First return map for the two-process model. The black line shows the return map, in other words for any value of sleep onset time on day , it shows the onset time of sleep on day , . The grey diagonal line is the line along which . One typical trajectory is plotted for showing the rapid convergence to the periodic cycle where modulo 1 day, the point at which the return map and the diagonal line intersect. The discontinuity is a result of the fact that neighbouring values of exist that lead to very different values for , as shown in (c). Parameter values for the two-process model are based on the PR model for the human sleep-wake cycle and can be found in (15).