Phase transitions in models of hierarchical modular networks
The brain’s efficient information processing motivates the critical brain hypothesis, which proposes that neural systems operate near a phase transition. However, standard neural network models often assess criticality through global measures, overlooking the local dynamics expected from the brain’s heterogeneous and modular organization. Here, we study a heterogeneous hierarchical modular model capable of displaying Griffiths phases, focusing on critical-like properties emerging from structural heterogeneity.
Analysis of activity time series revealed scaling behavior and a broadening of intrinsic timescales, consistent with critical slowing down. Modular sampling showed local specialization, with a hierarchy of timescales across network levels. Neuronal avalanche exponents followed a linear distribution, in agreement with previous experimental observations. The model also showed optimized information transmission, reflected in a maximum dynamic range, without requiring fine tuning. Finally, localized stimulation demonstrated that even systems undergoing a second-order phase transition can display strong local and global dynamic range gains when stimulated at intermediate or deep hierarchical levels.
Overall, this work suggests that structural heterogeneity can generate localized and specialized brain dynamics through modular network organization.
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