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

Abstract: 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.