Sleep is widely associated with homeostatic recovery, local use-dependent regulation, and state-dependent reorganization of network interactions. This manuscript proposes the Dynamical Threshold Theory of Sleep, a mathematical and computational prototype in which a multicellular biological system is represented as a network of adaptively coupled oscillatory elements with local homeostatic load, local sleep propensity, and selectively protected interactions.In this framework, wakefulness is modeled as a noisy adaptive synchronization regime under continued perturbation, whereas sleep emerges when the joint accumulation of local load and degradation of local coherence drive the system across a collective dynamical threshold into a sleep-dominant renormalization phase. To avoid the unbounded-coupling pathology of naive adaptive phase-oscillator models, the sleep-dominant subsystem is formulated as a bounded gradient flow of a reduced free energy.Numerical proof-of-concept simulations on hierarchical modular small-world networks reproduce three central features of the proposed framework: spatially heterogeneous accumulation of homeostatic burden, rapid growth of mean sleep propensity into a sleep-dominant regime, and bounded global downscaling of mean coupling strength toward finite fixed points. Additional analyses indicate that edges with stronger pre-sleep protection are preferentially preserved during sleep, consistent with selective down-selection rather than uniform weakening.This manuscript should be read strictly as a reduced network-dynamical prototype for sleep-like recovery transitions in adaptive multicellular systems. It is not medical advice, not a clinical sleep model, not a diagnostic or treatment tool, and not a claim of validation against human or animal sleep data.