Critical behaviour of the stochastic Wilson-Cowan model

Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version the celebrated Wilson-Cowan model has been widely studied as a system spiking neurons reproducing non-trivial neural activity, from avalanche dynamics to oscillatory behaviours. However, what extent such phenomena are related presence genuine point remains elusive. Here we address this central issue, providing analytical results in linear approximation extensive numerical analysis. In particular, present supporting existence bona fide point, where second-order-like phase transition occurs, scaling size diverging relaxation time-scale. Moreover, our study shows that observed behaviour falls within universality class mean-field branching process, exponents duration distributions are, respectively, 3/2 2. We also provide an accurate analysis function total number neurons, focusing on time correlation functions firing rate wide range parameter space.