Dynamical properties of the two-process model for sleep-wakecycles in infantile autism

The two-process model is a scheme for the timing of sleep that consists of homeostatic(Process S) and circadian (Process C) variables. The two-process modelexhibits abnormal sleep patterns such as internal desynchronization or sleep fragmentation.Early infants with autism often experience sleep difficulties. Large dayby-day changes are found in the sleep onset and waking times in autistic children.Frequent night waking is a prominent property of their sleep. Further, the sleepduration of autistic children is often fragmented. These sleep patterns in infantswith autism are not fully understood yet. In the present study, the sleep patternsin autistic children were reproduced by a modified two-process model using nonlinearanalysis. A nap term was introduced into the original two-process model toreproduce the sleep patterns in early infants. The nap term and the time course ofProcess S are mentioned in the present study. Those parameters led to bifurcation ofthe sleep-wake cycle in the modified two-process model. In a certain range of theseparameter sets, a small external noise was amplified, and an irregular sleep-wakecycle appeared. The short duration of sleep led to another irregular sleep onsetor waking. Consequently, an irregular sleep-wake cycle appeared in early infantileautism