@article{dec21,
author = {De Candia A, and Sarracino A., and Apicella I., and de Arcangelis L.,},
pages = {1},
title = {Critical behaviour of the stochastic Wilson-Cowan model},
note = {Articolo in rivista},
issn = {1553-734X},
journal = {PLOS COMPUTATIONAL BIOLOGY},
doi = {10.1371/journal.pcbi.1008884},
year = {2021},
abstract = {Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with
scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-
Cowan model has been widely studied as a system of spiking neurons reproducing
non-trivial features of the neural activity, from avalanche dynamics to oscillatory behaviours.
However, to what extent such phenomena are related to the presence of a genuine critical
point remains elusive. Here we address this central issue, providing analytical results in the
linear approximation and extensive numerical analysis. In particular, we present results supporting
the existence of a bona fide critical point, where a second-order-like phase transition
occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a
diverging relaxation time-scale. Moreover, our study shows that the observed critical behaviour
falls within the universality class of the mean-field branching process, where the exponents
of the avalanche size and duration distributions are, respectively, 3/2 and 2. We also
provide an accurate analysis of the system behaviour as a function of the total number of
neurons, focusing on the time correlation functions of the firing rate in a wide range of the
parameter space.}
}