  We model spontaneous cortical activity with a network of coupled spiking
units, in which multiple spatio-temporal patterns are stored as dynamical
attractors. We introduce an order parameter, which measures the overlap
(similarity) between the activity of the network and the stored patterns. We
find that, depending on the excitability of the network, different working
regimes are possible. For high excitability, the dynamical attractors are
stable, and a collective activity that replays one of the stored patterns
emerges spontaneously, while for low excitability, no replay is induced.
Between these two regimes, there is a critical region in which the dynamical
attractors are unstable, and intermittent short replays are induced by noise.
At the critical spiking threshold, the order parameter goes from zero to one,
and its fluctuations are maximized, as expected for a phase transition (and as
observed in recent experimental results in the brain). Notably, in this
critical region, the avalanche size and duration distributions follow power
laws. Critical exponents are consistent with a scaling relationship observed
recently in neural avalanches measurements. In conclusion, our simple model
suggests that avalanche power laws in cortical spontaneous activity may be the
effect of a network at the critical point between the replay and non-replay of
spatio-temporal patterns.
