Research Project Title

A Mathematical Analysis of Sleep Cycles and Circadian Rhythms

Session Type

Traditional Paper Presentation

Research Project Abstract

We analyzed the results found when comparing a nonlinear model involving coupled circadian oscillators to pooled data of test subjects in “free-run” sleep patterns. By non-dimensionalizing the model, we were able to determine conditions for which internal and external synchronization would be established. Based on those conditions, linear stability analysis reveals how sleep and circadian phases differ during external synchrony. Because of the simplicity of the model, we were also able to write the phase difference explicitly as function of time, which was used to test the relationship between circadian phase and sleep duration. This model reflected the pooled data well except on one account: timing of sleep onset in relation to circadian phase. We proposed a modification to the original model to correct for this discrepancy.

Session Number

RS3

Location

Weyerhaeuser 205

Abstract Number

RS3-d

This document is currently not available here.

COinS
 
Apr 28th, 9:15 AM Apr 28th, 10:45 AM

A Mathematical Analysis of Sleep Cycles and Circadian Rhythms

Weyerhaeuser 205

We analyzed the results found when comparing a nonlinear model involving coupled circadian oscillators to pooled data of test subjects in “free-run” sleep patterns. By non-dimensionalizing the model, we were able to determine conditions for which internal and external synchronization would be established. Based on those conditions, linear stability analysis reveals how sleep and circadian phases differ during external synchrony. Because of the simplicity of the model, we were also able to write the phase difference explicitly as function of time, which was used to test the relationship between circadian phase and sleep duration. This model reflected the pooled data well except on one account: timing of sleep onset in relation to circadian phase. We proposed a modification to the original model to correct for this discrepancy.