Sleep is essential for the maintenance of the brain and the body, yet many features of sleep are poorly understood and mathematical models are an important tool for probing proposed biological mechanisms. The most well-known mathematical model of sleep regulation, the two-process model, models the sleep-wake cycle by two oscillators: a circadian oscillator and a homeostatic oscillator. An alternative, more recent, model considers the mutual inhibition of sleep promoting neurons and the ascending arousal system regulated by homeostatic and circadian processes. Here we show there are fundamental similarities between these two models. The implications are illustrated with two important sleep-wake phenomena. Firstly, we show that in the two-process model, transitions between different numbers of daily sleep episodes can be classified as grazing bifurcations. This provides the theoretical underpinning for numerical results showing that the sleep patterns of many mammals can be explained by the mutual inhibition model. Secondly, we show that when sleep deprivation disrupts the sleep-wake cycle, ostensibly different measures of sleepiness in the two models are closely related. The demonstration of the mathematical similarities of the two models is valuable because not only does it allow some features of the two-process model to be interpreted physiologically but it also means that knowledge gained from study of the two-process model can be used to inform understanding of the behaviour of the mutual inhibition model. This is important because the mutual inhibition model and its extensions are increasingly being used as a tool to understand a diverse range of sleep-wake phenomena such as the design of optimal shift-patterns, yet the values it uses for parameters associated with the circadian and homeostatic processes are very different from those that have been experimentally measured in the context of the two-process model.
This research output has an Altmetric Attention Score of 12. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 06 January 2026.
All research outputs
#4,086,959
of 34,377,743 outputs
Outputs from PLOS ONE
#41,444
of 224,581 outputs
Outputs of similar age
#33,450
of 271,791 outputs
Outputs of similar age from PLOS ONE
#872
of 5,007 outputs
Altmetric has tracked 34,377,743 research outputs across all sources so far. Compared to these this one has done well and is in the 88th percentile: it's in the top 25% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 224,581 research outputs from this source. They typically receive a lot more attention than average, with a mean Attention Score of 17.2. This one has done well, scoring higher than 81% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 271,791 tracked outputs that were published within six weeks on either side of this one in any source. This one has done well, scoring higher than 87% of its contemporaries.
We're also able to compare this research output to 5,007 others from the same source and published within six weeks on either side of this one. This one has done well, scoring higher than 82% of its contemporaries.
