Dual homeostatic and circadian resonance shapes REM episode duration.

Rapid eye movement (REM) sleep is influenced by homeostatic and circadian processes, but why distinct REM episode-duration profiles-bell-shaped, flattened, amplified, near-linear, and bimodal-occur remains unresolved. The wave model of sleep dynamics treats REM sleep as a coherent sleep-wake mixed state stabilized by resonance between sleep and wake probability waves near their homeostatic equilibrium region. Here we extend this framework by adding a circadian REM-promoting resonance anchored to biological time. REM duration was modeled as a compound resonance generated by two fixed curve shapes: a broad homeostatic resonance and a narrower Lorentzian circadian resonance. Only amplitude, reflecting prior-wake-dependent state instability, and relative phase alignment were varied. This constrained model reproduced REM-duration profiles during regular sleep, chronic sleep extension, and post-deprivation recovery. Baseline and recovery sleep followed a conserved empirical compound resonance curve, indicating preservation of the equilibrium/resonance peak after acute sleep loss. The predicted high-instability extension and asymmetric REM profile provide a physiological estimate of accumulated sleep deficit as additional recovery time required to return toward the sleep-wake equilibrium setpoint. Independent validation came from a 525-night longitudinal extended-sleep dataset, in which reduced resonance overlap predicted mid-sleep wake clustering and sleep-continuity instability. These findings identify REM episode duration as a quantitative marker of homeostatic-circadian alignment, recovery need, and setpoint regulation.