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Friday, November 9, 2018 at 3:30pm
The temporal structure of human sleep changes across development as sleep consolidates from the fragmented sleep of infants to the single nighttime sleep period typical in adults. This transition is likely driven by developmentally-mediated slowing in the rates of accumulation and dissipation of the homeostatic sleep drive, the physiological drive to sleep that increases with time spent awake. Experimental advances in identifying the neurophysiology of sleep-wake regulation have led to the formulation of physiologically-based mathematical models that describe the dynamics of neuronal interactions within the sleep-wake regulatory network and their modulation by homeostatic and circadian drives. Given the periodicity of regular, entrained sleep-wake behavior, one-dimensional circle maps—defined analytically in some cases and numerically in others—may be used to represent the dynamics of the full sleep-wake network model. In this talk I will describe mathematical modeling of sleep, the piecewise continuous maps that represent model dynamics, and bifurcations arising in these maps. Specifically, tracking bifurcations as homeostatic sleep drive time constants are varied provides insight into the structure underlying the consolidation of sleep from many to one sleep period per day. This analysis has implications for understanding the dynamics of the transition from napping to non-napping behavior in early childhood.
Cecilia Diniz Behn is an Assistant Professor in the Department of Applied Mathematics and Statistics at Colorado School of Mines. She also holds an appointment as an Adjoint Assistant Professor of Pediatrics at the University of Colorado School of Medicine. She received her PhD in Mathematics from Boston University and conducted postdoctoral work at Harvard Medical School and the University of Michigan. Her research focuses on dynamical systems and multiscale mathematical modeling with applications in metabolism, sleep, and circadian rhythms.