Fig. 4: Power-law distributions of neuronal avalanche sizes and durations.
From: Influence of topology on the critical behavior of hierarchical modular neuronal networks
a Distribution of avalanche sizes for a network with N = 8192 neurons across various hierarchical levels. The dashed reference line follows a power-law \(\propto {s}^{-{\tau }_{s}}\), with the exponent for the avalanche sizes, τs ≈ 1.5, indicating criticality. For both Erdős-Rényi (ER) and K neighbors per neuron (KN) topologies, the distributions for all hierarchical levels collapse onto a single curve. b Distribution of avalanche durations for different hierarchical levels H with N = 8192 neurons. The dashed reference line follows a power-law \(\propto {d}^{-{\tau }_{d}}\), with exponent for the avalanche durations, τd ≈ 2.0, also suggesting criticality. The reference line was obtained using the least-squares regression method. In all cases, the long tails in the distributions are due to large-scale, long-duration avalanches, known as “dragon kings'', which suggests the system is in a slightly supercritical state.
