  Many experimental results, both in-vivo and in-vitro, support the idea that
the brain cortex operates near a critical point, and at the same time works as
a reservoir of precise spatio-temporal patterns. However the mechanism at the
basis of these observations is still not clear. In this paper we introduce a
model which combines both these features, showing that scale-free avalanches
are the signature of a system posed near the spinodal line of a first order
transition, with many spatio-temporal patterns stored as dynamical metastable
attractors. Specifically, we studied a network of leaky integrate and fire
neurons, whose connections are the result of the learning of multiple
spatio-temporal dynamical patterns, each with a randomly chosen ordering of the
neurons. We found that the network shows a first order transition between a low
spiking rate disordered state (down), and a high rate state characterized by
the emergence of collective activity and the replay of one of the stored
patterns (up). The transition is characterized by hysteresis, or alternation of
up and down states, depending on the lifetime of the metastable states. In both
cases, critical features and neural avalanches are observed. Notably, critical
phenomena occur at the edge of a discontinuous phase transition, as recently
observed in a network of glow lamps.
