De Candia, A. | Search bioRxiv

bioRxiv2025

Symmetry breaking and avalanche shapes in modular neural networks

Modularity is as a key characteristic of structural and functional brain networks across species and spatial scales. We investigate the stochastic Wilson-Cowan model on a modular network in which synaptic strengths differ between intra-module and inter-module connections. The system exhibits a rich phase diagram comprising symmetric (SL and SH) and "broken symmetry" (B1, B2, ...) phases. The phase SL (SH) is characterized by the same low (high) activity in all the modules, while the Bm phases are characterized by a high activity in m modules and low activity in the remaining modules. Between SL and SH, and between SL and B1, there are two lines of critical points, where the system shows a critical behaviour, with power law distributions in the avalanches. Along these lines, avalanche shapes differ systematically: they are symmetric or right-skewed at the SL-SH transition, but can become left-skewed over intermediate durations along the SL-B1 critical line. These results provide a theoretical framework that accounts for both symmetric and left-skewed neural avalanche shapes observed experimentally, linking modular organization to critical brain dynamics.

neuroscience↗

bioRxiv2021

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 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. Author summaryNetworks of spiking neurons are introduced to describe some features of the brain activity, which are characterized by burst events (avalanches) with power-law distributions of size and duration. The observation of this kind of noisy behaviour in a wide variety of real systems led to the hypothesis that neuronal networks work in the proximity of a critical point. This hypothesis is at the core of an intense debate. At variance with previous claims, here we show that a stochastic version of the Wilson-Cowan model presents a phenomenology in agreement with the existence of a bona fide critical point for a particular choice of the relative synaptic weight between excitatory and inhibitory neurons. The system behaviour at this point shows all features typical of criticality, such as diverging timescales, scaling with the system size and scale-free distributions of avalanche sizes and durations, with exponents corresponding to the mean-field branching process. Our analysis unveils the critical nature of the observed behaviours.

neuroscience↗