Stochastic Dynamics of Consciousness as a Multi-Scale Regime: A Metabolic–Integrative Formulation

Canonical conscious and unconscious brain states occupy a restricted region of a joint metabolic–integration state space, bounded by a lower metabolic limit near ~44–46% of normal cortical glucose metabolism and a perturbational complexity threshold near PCI ≈ 0.31. Existing formulations treat this boundary as a deterministic threshold, yet the underlying physiology is multi-scale and stochastic, so abrupt cut-offs are unlikely to reflect the true dynamical structure of state transitions. Here we develop a stochastic, multi-scale dynamical formulation of the metabolic–integrative framework in which fast neural dynamics capable of bistability and noise-driven switching are embedded within slower metabolic and systemic regulators (endocrine, immune, interoceptive/autonomic). Using a fold-normal-form neural subsystem coupled to a metabolic control parameter and a systemic state, we recast the consciousness boundary as a probabilistic regime defined by the occupancy of a high-integration attractor basin. Numerical simulation reproduces the empirically observed quadrant organization of canonical states — including the off-diagonal placement of NREM sleep (preserved metabolism, reduced integration) — and generates four dynamical signatures that emerge from the coupled stochastic system rather than from calibration: graded regime occupancy across the transition band (M₅₀ ≈ 0.45), direction-dependent hysteresis between induction and emergence (ΔM ≈ 0.07), intermittent stochastic switching near the bistable centre, and a monotonic systemic-state-dependent shift of the effective metabolic threshold (≈ 0.24 across the simulated systemic range, with monotonic dependence on systemic state; ρ = +1.00). These signatures convert the framework into a falsifiable program combining FDG-PET, TMS–EEG, and peripheral biomarkers, and identify systemic-state-dependent threshold shift as the prediction most discriminating from generic fold-bifurcation accounts.