Understanding the Sleep Wake Cycle
Biomathematics Summer Institute at NCA&T sponsered by NSF TALENT-21 Program in Greensboro, NC
Mentors: Dr. Liping Liu & Dr. Choongseok Park
Team Members: Cameron Bernado & Maleek Richardson
Summer 2015

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Abstract

The sleep/wake cycle is the species specific biological pattern of alternatingsleep and wakefulness, which in humans is roughly 8 hours of nocturnal sleep and16 hours of daytime activity. Sleep is important not only because it provides restand recovery, but also allows dynamic biological activities that are vital to our everyday health to occur. In this project, we present a biologically based mathe-matical model. This model accounts for features including the timing of sleep andwakefulness. We use the model in investigating how wake-promoting neurons in-hibit sleep-promoting neurons, and conversely how sleep-promoting neurons inhibitwake-promoting neurons. This mechanism of excitation and inhibition generates a"flip–flop" switch, which we further investigate based on previously studied mod-els. Simulations performed with the above differential equations generates patternsthat support the flip–flop switch. Analyzing the results generated from those sim-ulations help explain mathematical phenomena, such as bifurcation, that exist inthe model. A more detailed analysis leads to better insight on the mathematicalmechanisms and biological processes behind the sleep/wake cycle.