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.