Dynamical properties of the two-process model for sleep-wake cycles 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 model exhibits abnormal sleep patterns such as internal desynchronization or sleep fragmentation. Early infants with autism often experience sleep difficulties. Large day-by-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 sleep duration of autistic children is often fragmented. These sleep patterns in infants with autism are not fully understood yet. In the present study, the sleep patterns in autistic children were reproduced by a modified two-process model using nonlinear analysis. A nap term was introduced into the original two-process model to reproduce the sleep patterns in early infants. The nap term and the time course of Process S are mentioned in the present study. Those parameters led to bifurcation of the sleep-wake cycle in the modified two-process model. In a certain range of these parameter sets, a small external noise was amplified, and an irregular sleep-wake cycle appeared. The short duration of sleep led to another irregular sleep onset or waking. Consequently, an irregular sleep-wake cycle appeared in early infantile autism.