  Understanding the origin, nature, and functional significance of complex
patterns of neural activity, as recorded by diverse electrophysiological and
neuroimaging techniques, is a central challenge in neuroscience. Such patterns
include collective oscillations emerging out of neural synchronization as well
as highly heterogeneous outbursts of activity interspersed by periods of
quiescence, called "neuronal avalanches." Much debate has been generated about
the possible scale invariance or criticality of such avalanches and its
relevance for brain function. Aimed at shedding light onto this, here we
analyze the large-scale collective properties of the cortex by using a
mesoscopic approach following the principle of parsimony of Landau-Ginzburg.
Our model is similar to that of Wilson-Cowan for neural dynamics but crucially,
includes stochasticity and space; synaptic plasticity and inhibition are
considered as possible regulatory mechanisms. Detailed analyses uncover a phase
diagram including down-state, synchronous, asynchronous, and up-state phases
and reveal that empirical findings for neuronal avalanches are consistently
reproduced by tuning our model to the edge of synchronization. This reveals
that the putative criticality of cortical dynamics does not correspond to a
quiescent-to-active phase transition as usually assumed in theoretical
approaches but to a synchronization phase transition, at which incipient
oscillations and scale-free avalanches coexist. Furthermore, our model also
accounts for up and down states as they occur (e.g., during deep sleep). This
approach constitutes a framework to rationalize the possible collective phases
and phase transitions of cortical networks in simple terms, thus helping to
shed light on basic aspects of brain functioning from a very broad perspective.
