Hysteresis, neural avalanches, and critical behavior near a first-order transition of a spiking neural network.

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 spatiotemporal 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 spatiotemporal 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 spatiotemporal 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.