Potential formulation of sleep dynamics

A physiologically based model of the mechanisms that control the human sleep-wake cycle is formulated in terms of an equivalent nonconservative mechanical potential. The potential is analytically simplified and reduced to a quartic two-well potential, matching the bifurcation structure of the original model. This yields a dynamics-based model that is analytically simpler and has fewer parameters than the original model, allowing easier fitting to experimental data. This model is first demonstrated to semiquantitatively match the dynamics of the physiologically based model from which it is derived, and is then fitted directly to a set of experimentally derived criteria. These criteria place rigorous constraints on the parameter values, and within these constraints the model is shown to reproduce normal sleep-wake dynamics and recovery from sleep deprivation. Furthermore, this approach enables insights into the dynamics by direct analogies to phenomena in well studied mechanical systems. These include the relation between friction in the mechanical system and the timecourse of neurotransmitter action, and the possible relation between stochastic resonance and napping behavior. The model derived here also serves as a platform for future investigations of sleep-wake phenomena from a dynamical perspective.