Nonsmooth Maps and the Fast-Slow Dynamics of Sleep-Wake Regulation: Part I
Sleep-wake regulation is an example of a system with multiple timescales, with switching between sleep and wake states occurring in minutes but the states of wake or sleep usually existing for some hours. Here, we discuss some general features of models of sleep-wake regulation. We show that some typical models of sleep-wake regulation can be reduced to one-dimensional maps with discontinuities, and show that this reduction is useful in understanding some of the dynamical behaviour seen in sleep-wake models.
The authors thank the Centre de Recerca Matemàtica for the opportunity to work with each other and other participants of the intensive programme on Advances in Nonsmooth Dynamics. ACS and GD are indebted to Prof. Derk-Jan Dijk of the Surrey Sleep Research Centre at the University of Surrey for introducing them to the area of mathematical modelling of sleep-wake regulation.
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