A Mathematical Analysis of Sleep Cycles and Circadian Rhythms
Faculty Sponsor
Richard Cangelosi
cangelosi@gonzaga.edu
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
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.
