In adult mammalian species, sleep is composed of several micro-sleep bouts whichare exponentially distributed and micro-wake bouts which follow a power law. In
infant rats both sleep and wake bouts follow an exponential law, only as the animal
develops the wake bout times develop the heavy tail of a power law.
Based on a survey of experimental findings, we identify the populations of neurons
responsible for the state change behavior and propose a connectivity diagram consistent with the known neurophysiology. We suggest a new general modeling approach where individual populations of neurons are modeled as Poisson processes whose rates are stochastic processes and satisfy a system of stochastic differential equations. We also suggest a canonical map from the connectivity diagram to the Poisson process model.
The analysis of the stochastic dynamical system is based on an appropriate deterministic approximation. The deterministic dynamical system is analyzed using standard results and these results are then used to make predictions about the stochastic system. The model shows the appropriate behavior of random switching between sleep and wake and how the probability of this switching behavior changes with age. We find that a necessary condition for the bout distribution in the stochastic system to change from exponential to power law is that the deterministic system has a bifurcation from one stable fixed point to two stable fixed points.
Finally, in order to compare the theoretical predictions with experimental data
we develop algorithms for parameter estimation and for comparison of the simulated
and the experimental data.