Map-based approaches for investigating sleep/wake dynamics

Abstract

A homeostatic need for sleep increases with time awake and decreases during sleep. When the build up and recovery of sleepiness occurs sufficiently quickly, a person experiences two sleep cycles, a nap as well as nighttime sleep, each day. To investigate the transition between one and two sleep cycles per day, we consider the bifurcations of a previously developed model for human sleep/wake dynamics. As the time constants related to the build up and recovery of sleepiness are decreased, the system exhibits an incremental increase in the number of sleep cycles per day. Using a one-dimensional map to represent the dynamics of the system, we relate this map to a normal form for a piecewise continuous system which undergoes a border collision bifurcation, and provide numerical evidence for period-adding behavior. This analysis has implications for understanding the dynamics of the transition from napping to non-napping behavior in early childhood.