Mechanistic Modeling of Sleep-Wake Transitions via Circadian-Modulated Threshold Dynamics
Human sleep-wake cycles emerge from complex interactions between homeostatic sleep pressure and circadian rhythms. In this study, we extend the Phillips-Robinson model by introducing circadian-dependent dynamic thresholds for sleep and wake transitions, yielding a more physiologically grounded framework for sleep regulation. Using bifurcation analysis, we show that the transition from sustained wakefulness to rhythmic sleep-wake cycles is governed by a saddle-node on invariant circle (SNIC) bifurcation, and that these oscillations become entrained to external 24 h light-dark cues. We analytically derive circadian-modulated sleep and wake thresholds, revealing how the interaction between circadian and homeostatic drives governs sleep-wake transitions. Our model captures key physiological phenomena, including: (1) the onset and entrainment of sleep-wake rhythms, (2) immediate sleep onset and partial rebound following sleep deprivation, and (3) sleep fragmentation under shift work-like conditions. These results offer new mechanistic insights into how circadian misalignment alters sleep timing and quality. Together, our findings establish an updated theoretical framework for modeling sleep-wake regulation in both natural and disrupted environments, with implications for shift work management, sleep disorder interventions, and personalized chronotherapy.