Nonlinear-dynamics theory of up-down transitions in neocortical neural networks.

The neurons of the neocortex show ~1-Hz synchronized transitions between an active up state and a quiescent down state. The up-down state transitions are highly coherent over large sections of the cortex, yet they are accompanied by pronounced, incoherent noise. We propose a simple model for the up-down state oscillations that allows analysis by straightforward dynamical systems theory. An essential feature is a nonuniform network geometry composed of groups of excitatory and inhibitory neurons with strong coupling inside a group and weak coupling between groups. The enhanced deterministic noise of the up state appears as the natural result of the proximity of a partial synchronization transition. The synchronization transition takes place as a function of the long-range synaptic strength linking different groups of neurons.