A simple model for the origin of quasiperiodic ultradian rhythms in sleep-wake state in the rat

In a recent study,1 ultradian rhythms of rat sleep-wake behavior were found, using several methods of time series analysis, to be “quasiperiodic.” That is, ultradian period varied apparently randomly around a mean of approximately 4 h, with no relationship between ultradian period and time of day. Here it is proposed that a simple two-oscillator model can explain the quasiperiodic characteristic of these rhythms. Specifically, in this model a periodic oscillator interacts with a stochastic oscillator to generate a behavioral pattern in which the period and amplitude of the simulated ultradian waves vary randomly around an average value. Preliminary simulations support the plausibility of the model; simulated waveforms were closely similar to behavior patterns observed in adult male rats. It is hypothesized that ultradian rhythms in sleep-wake behavior may arise from a periodic feedback loop (e.g., the sleep-wake homeostat) coupled to a stochastic sleep-wake “flip-flop” switch.