REM sleep complicates period adding bifurcations from monophasic to polyphasic sleep behavior in a sleep-wake regulatory network model for human sleep

The structure of human sleep changes across development as it consolidates from the polyphasic sleep of infants to the single nighttime sleep period typical in adults. Across this same developmental period, time scales of the homeostatic sleep drive, the physiological drive to sleep that increases with time spent awake, also change and presumably govern the transition from polyphasic to monophasic sleep behavior. Using a physiologically-based, sleep-wake regulatory network model for human sleep, we investigated the dynamics of wake, rapid eye movement (REM) sleep, and non-REM (NREM) sleep during this transition by varying the homeostatic sleep drive time constants. Previously, we introduced an algorithm for constructing a one-dimensional circle map that represents the dynamics of the full sleep-wake network model. By tracking bifurcations in the piecewise continuous circle map as the homeostatic sleep drive time constants are varied, we establish evidence for a border collision bifurcation that results in period-adding-like behavior in the number of sleep cycles per day. Interestingly, this bifurcation is preceded by bifurcations in the number of REM bouts per sleep cycle that exhibit truncated period-adding-like behavior. The interaction of these bifurcations in numbers of sleep episodes and numbers of REM bouts per sleep episode generate non-monotonic variation in sleep cycle patterns as well as quasi-periodic patterns during the transition from polyphasic to monophasic sleep behavior. This analysis may have implications for understanding changes in sleep in early childhood when preschoolers transition from napping to non-napping behavior, and the wide interindividual variation observed during this transition.