Influence of topology on the critical behavior of hierarchical modular neuronal networks

Abstract Understanding how the brain maintains stable, yet flexible, activity is a central question in neuroscience. While previous work suggests that criticality–when neurons are poised near a phase transition –supports optimal brain function, how network architecture affects this condition remains unclear. Here, we study hierarchical modular neuronal networks composed of stochastic spiking neurons with adaptive dynamics. We show that network topology significantly influences critical behavior, with sparse modular architectures sustaining criticality more robustly than fully connected ones. Our simulations reveal that homeostatic mechanisms can stabilize activity near criticality, even as modular interactions introduce structural inhomogeneities. These inhomogeneities can produce quasicritical dynamics and Griffiths-like phases, broadening the range of near-critical behavior. Our work highlights the role of structural organization in shaping emergent brain dynamics and offers new insights into how biological networks may tune themselves to operate near criticality.