Nonlinear Dynamics of Sleep-Stage Transitions: Evidence for Threshold Gating and Hysteresis in Human EEG

Background: Theories of consciousness often assume linear transitions between states—smooth movement along an entropy or integration axis. This assumption remains empirically untested for natural state changes such as sleep. Methods: We analysed 773 sleep-stage transitions (Wake↔N1↔N2↔N3) in 10 healthy adults using a Consciousness Gradient Index (CGI) derived from scalp EEG. CGI combines state-appropriate measures of neural integration with temporal stability, tracked continuously across ±300-second windows around scored transition boundaries. We compared linear versus sigmoid (tanh) model fits, tested for hysteresis between deepening and lightening trajectories, and examined spindle-CGI temporal coupling at the N1→N2 boundary. Findings were validated against Lempel-Ziv complexity (LZc) and through permutation and bootstrap testing. Results: Sigmoid models outperformed linear models for 5/6 transition types on grand-averaged trajectories (tanh R² = 0.79–0.85 vs linear R² = 0.44–0.67 for deepening transitions). Within-subject analysis confirmed nonlinear superiority in 100% of subjects for Wake→N1 and 70% for N1→N2. Significant hysteresis was detected at both N1↔N2 (z = 24.7, p < 0.0001) and N2↔N3 (z = 3.0, p = 0.014) boundaries—deepening and lightening followed different CGI paths. Sleep spindle onset preceded CGI inflection by 45.9 seconds (95% CI: −62 to −31 s, p = 0.0001), consistent with a gating mechanism. LZc converged with CGI on 5/6 model selections and confirmed N2↔N3 hysteresis, while N1↔N2 hysteresis was CGI-specific, reflecting spindle-mediated dynamics invisible to broadband complexity measures. Conclusions: Sleep-stage transitions follow nonlinear threshold dynamics with path-dependent hysteresis, challenging linear models of consciousness state change. Falling asleep and waking up are fundamentally asymmetric processes: deepening involves spindle-gated thresholds, while lightening follows more gradual trajectories. These findings support an attractor-basin framework for consciousness states and have implications for anaesthesia monitoring, consciousness theory, and the characterisation of altered states.