Georgia Institute of Technology College of Sciences

Link: https://gatech.zoom.us/j/91390791493?pwd=QnpaWHNEOHZTVXlZSXFkYTJ0b0Q0UT09

Abstract: The timing of human sleep is strongly modulated by the 24 hour circadian rhythm, our internal biological clock, and the homeostatic sleep drive, one’s need for sleep which depends on prior awakening. The parameters dictating the evolution of the homeostatic sleep drive may vary with development and have been identified as important parameters for generating the transition from multiple sleeps to a single sleep episode per day. We employ piecewise-smooth ODE-based mathematical models to analyze developmentally-mediated transitions of sleep-wake patterns, including napping and non-napping behaviors. Our framework includes the construction of a circle map that captures the timing of sleep onsets on successive days. Analysis of the structure and bifurcations in the map reveals changes in the average number of sleep episodes per day in a period-adding-like structure. In two-state models of sleep-wake regulation, namely models that generate sleep and wake states, we observe saddle-node and border collision bifurcations in the maps. However, in our three-state model of sleep-wake regulation, which captures wake, rapid eye movement (REM) sleep, and non-REM sleep, these sequences are disrupted by period-doubling bifurcations and can exhibit bistability.