Staal, J.J. (2016) Sleep wake models. Bachelor's Thesis, Mathematics.
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Abstract
In this thesis we are going to make a comparison between two different sleep models. The two process model is based on a certain ”sleep pressure”. The stress increases when a person is awake and the stress decreases during sleep. When awake, the stress will reach an upper level and the person will turn to sleep untill a lower bound is reached. However this upper and lower bounds depend on external factors(e.g. day and night) regulated by the internal clock and is a 24 hour periodic function. The other model, the PR model, is also based on a sleep pressure, but now depending on two different brain areas which are active either during sleep or while awake and the interaction between those two areas. This can be represented by a three-dimensional system of differential equations where each equation represent either one of the two brain areas or the sleep pressure. We will obtain a slow-fast system and therefore we are comparing these models by taking the slow time limit and the hard switch limit in the PR model, the concept of these limits will be explained. Furthermore we are going to analyse the dynamics on the slow manifold of the PR model.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Feb 2018 08:23 |
| Last Modified: | 15 Feb 2018 08:23 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/14325 |
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