  Complex coherent dynamics is present in a wide variety of neural systems. A
typical example is the voltage transitions between up and down states observed
in cortical areas in the brain. In this work, we study this phenomenon via a
biologically motivated stochastic model of up and down transitions. The model
is constituted by a simple bistable rate model, where the synaptic current is
modulated by short-term synaptic processes which introduce stochasticity and
temporal correlations. A complete analysis of our model, both with mean-field
approaches and numerical simulations, shows the appearance of complex
transitions between high (up) and low (down) neural activity states, driven by
the synaptic noise, with permanence times in the up state distributed according
to a power-law. We show that the experimentally observed large fluctuation in
up and down permanence times can be explained as the result of sufficiently
noisy dynamical synapses with sufficiently large recovery times. Static
synapses cannot account for this behavior, nor can dynamical synapses in the
absence of noise.
